Maths-

General

Easy

Question

# Polar of origin (0, 0) w.r.t. the circle touches the circle , if

Hint:

### In this question, we have to find the correct option if Polar of origin (0, 0) w. r. t. the circle touches the circle . As we know that the polar of equation is 0. So, using this and putting P (0,0), we can find a equation for perpendicular distance of a point P and center (0,0) we can find the value of r and solving that we will get the correct option.

## The correct answer is:

### Related Questions to study

physics-

### Electrons ejected from the surface of a metal, when light of certain frequency is incident on it, are stopped fully by a retarding potential of 3 volts Photo electric effect in this metallic surface begins at a frequency 6 x 1014s ^{-1} The frequency of the incident light in s^{-1} is [h=6 x 10^{-34}J-sec;charge on the electron=1.6x10^{-19}C]

### Electrons ejected from the surface of a metal, when light of certain frequency is incident on it, are stopped fully by a retarding potential of 3 volts Photo electric effect in this metallic surface begins at a frequency 6 x 1014s ^{-1} The frequency of the incident light in s^{-1} is [h=6 x 10^{-34}J-sec;charge on the electron=1.6x10^{-19}C]

physics-General

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### Trajectories of two projectiles are shown in figure. Let and be the time periods and and their speeds of projection. Then

Maximum height and time of flight depend on the vertical component of initial velocity

Here

Range

Here

Range

### Trajectories of two projectiles are shown in figure. Let and be the time periods and and their speeds of projection. Then

physics-General

Maximum height and time of flight depend on the vertical component of initial velocity

Here

Range

Here

Range

physics-

### A body is projected up a smooth inclined plane with a velocity from the point as shown in figure. The angle of inclination is and top of the plane is connected to a well of diameter 40 m. If the body just manages to cross the well, what is the value of ? Length of the inclined plane is , and

Let be the velocity acquired by the body at which will be moving making an angle with the horizontal direction. As the body just crosses the well so

or

or

Taking motion of the body from to along the inclined plane we have

As

or or

or

or

Taking motion of the body from to along the inclined plane we have

As

or or

### A body is projected up a smooth inclined plane with a velocity from the point as shown in figure. The angle of inclination is and top of the plane is connected to a well of diameter 40 m. If the body just manages to cross the well, what is the value of ? Length of the inclined plane is , and

physics-General

Let be the velocity acquired by the body at which will be moving making an angle with the horizontal direction. As the body just crosses the well so

or

or

Taking motion of the body from to along the inclined plane we have

As

or or

or

or

Taking motion of the body from to along the inclined plane we have

As

or or

Maths-

### The equation of the circumcircle of the triangle formed by the lines and y=0 is

### The equation of the circumcircle of the triangle formed by the lines and y=0 is

Maths-General

physics-

### Which of the substance or has the highest specific heat? The temperature time graph is shown

Substances having more specific heat take longer time to get heated to a higher temperature and longer time to get cooled.

If we draw a line parallel to the time axis then it cuts the given graphs at three different points. Corresponding points on the times axis shows that

If we draw a line parallel to the time axis then it cuts the given graphs at three different points. Corresponding points on the times axis shows that

### Which of the substance or has the highest specific heat? The temperature time graph is shown

physics-General

Substances having more specific heat take longer time to get heated to a higher temperature and longer time to get cooled.

If we draw a line parallel to the time axis then it cuts the given graphs at three different points. Corresponding points on the times axis shows that

If we draw a line parallel to the time axis then it cuts the given graphs at three different points. Corresponding points on the times axis shows that

physics-

### The figure shows a system of two concentric spheres of radii and and kept at temperatures and respectively. The radial rate of flow of heat in a substance between the two concentric spheres, is proportional to

To measure the radial rate of heat flow, we have to go for integration technique as here the area of the surface through which heat will flow is not constant.

Let us consider an element (spherical shell) of thickness d and radius as shown in figure. Let us first find the equivalent thermal resistance between inner and outer sphere.

Resistance of shell=

=

Rate of heat flow = H

=

=

Let us consider an element (spherical shell) of thickness d and radius as shown in figure. Let us first find the equivalent thermal resistance between inner and outer sphere.

Resistance of shell=

=

Rate of heat flow = H

=

=

### The figure shows a system of two concentric spheres of radii and and kept at temperatures and respectively. The radial rate of flow of heat in a substance between the two concentric spheres, is proportional to

physics-General

To measure the radial rate of heat flow, we have to go for integration technique as here the area of the surface through which heat will flow is not constant.

Let us consider an element (spherical shell) of thickness d and radius as shown in figure. Let us first find the equivalent thermal resistance between inner and outer sphere.

Resistance of shell=

=

Rate of heat flow = H

=

=

Let us consider an element (spherical shell) of thickness d and radius as shown in figure. Let us first find the equivalent thermal resistance between inner and outer sphere.

Resistance of shell=

=

Rate of heat flow = H

=

=

maths-

### If the line y = x + 3 meets the circle at A and B, then equation of the circle on AB as diameter is

### If the line y = x + 3 meets the circle at A and B, then equation of the circle on AB as diameter is

maths-General

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### An electric lamp is fixed at the ceiling of a circular tunnel as shown is figure. What is the ratio the intensities of light at base *A* and a point *B* on the wall

and

### An electric lamp is fixed at the ceiling of a circular tunnel as shown is figure. What is the ratio the intensities of light at base *A* and a point *B* on the wall

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and

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### The distance between a point source of light and a screen which is 60 *cm* is increased to 180 *cm*. The intensity on the screen as compared with the original intensity will be

### The distance between a point source of light and a screen which is 60 *cm* is increased to 180 *cm*. The intensity on the screen as compared with the original intensity will be

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Maths-

The pole of the straight line 9x + y – 28 = 0 with respect to the circle is

Let the coordinates of the pole be (h, k).

The equation of the circle is 2x

Dividing both sides of the equation by 2,we get

x

The equation of polar for the point having coordinates (h, k) is

h x + k y - 3/4 (x + h) + 5/4 (y+k) - 7/2 = 0 .

Simplifying the equation, it can be written as (4h - 3)x + (4k + 5)y + (-3h + 5k - 14).

We are given that the equation of the polar is 9x + y - 28 = 0.so, the above equation and this equation represent the same line. Comparing the coefficient of the line, we get

(4h - 3) /9 = (4k + 5) /1 = (-3h + 5k - 14) /-28

Taking the first and third expression, we get

(4h - 3) /9 = (-3h + 5k - 14) /-28 .

By cross multiplication, we get

Or, -28 (4h - 3) = 9 (-3h + 5k - 14)

Or, -112h + 84 = -27h + 45k - 126

Or, -112h + 27h - 45k = -126 - 84

Or, -85h - 45k = -210

Or, -5 ( 17h + 9k ) = -210

17h + 9k = 42 . . . (1)

Taking the second and third expression, we get

(4k + 5) /1 = ( -3h + 5k - 14) /-28

By cross multiplication, we get

-28 ( 4k + 5 ) = ( -3h + 5k - 14 )

-112k - 140 = -3h + 5k - 14

3h - 112k - 5k = -14 + 140

3h - 117k = 126 . . . (2)

By solving equation (1) × 13 and equation (2) .

h = 3

By putting the value of h in equation (1) , we get

K = -1 .

Therefore, the coordinates are (3, -1) .

Hence, the correct option is (a).

The equation of the circle is 2x

^{2}+ 2y^{2}- 3x + 5y - 7 = 0.Dividing both sides of the equation by 2,we get

x

^{2}+ y^{2}- 3/2 x + 5/2 y - 7/2 = 0.The equation of polar for the point having coordinates (h, k) is

h x + k y - 3/4 (x + h) + 5/4 (y+k) - 7/2 = 0 .

Simplifying the equation, it can be written as (4h - 3)x + (4k + 5)y + (-3h + 5k - 14).

We are given that the equation of the polar is 9x + y - 28 = 0.so, the above equation and this equation represent the same line. Comparing the coefficient of the line, we get

(4h - 3) /9 = (4k + 5) /1 = (-3h + 5k - 14) /-28

Taking the first and third expression, we get

(4h - 3) /9 = (-3h + 5k - 14) /-28 .

By cross multiplication, we get

Or, -28 (4h - 3) = 9 (-3h + 5k - 14)

Or, -112h + 84 = -27h + 45k - 126

Or, -112h + 27h - 45k = -126 - 84

Or, -85h - 45k = -210

Or, -5 ( 17h + 9k ) = -210

17h + 9k = 42 . . . (1)

Taking the second and third expression, we get

(4k + 5) /1 = ( -3h + 5k - 14) /-28

By cross multiplication, we get

-28 ( 4k + 5 ) = ( -3h + 5k - 14 )

-112k - 140 = -3h + 5k - 14

3h - 112k - 5k = -14 + 140

3h - 117k = 126 . . . (2)

By solving equation (1) × 13 and equation (2) .

h = 3

By putting the value of h in equation (1) , we get

K = -1 .

Therefore, the coordinates are (3, -1) .

Hence, the correct option is (a).

The pole of the straight line 9x + y – 28 = 0 with respect to the circle is

Maths-General

Let the coordinates of the pole be (h, k).

The equation of the circle is 2x

Dividing both sides of the equation by 2,we get

x

The equation of polar for the point having coordinates (h, k) is

h x + k y - 3/4 (x + h) + 5/4 (y+k) - 7/2 = 0 .

Simplifying the equation, it can be written as (4h - 3)x + (4k + 5)y + (-3h + 5k - 14).

We are given that the equation of the polar is 9x + y - 28 = 0.so, the above equation and this equation represent the same line. Comparing the coefficient of the line, we get

(4h - 3) /9 = (4k + 5) /1 = (-3h + 5k - 14) /-28

Taking the first and third expression, we get

(4h - 3) /9 = (-3h + 5k - 14) /-28 .

By cross multiplication, we get

Or, -28 (4h - 3) = 9 (-3h + 5k - 14)

Or, -112h + 84 = -27h + 45k - 126

Or, -112h + 27h - 45k = -126 - 84

Or, -85h - 45k = -210

Or, -5 ( 17h + 9k ) = -210

17h + 9k = 42 . . . (1)

Taking the second and third expression, we get

(4k + 5) /1 = ( -3h + 5k - 14) /-28

By cross multiplication, we get

-28 ( 4k + 5 ) = ( -3h + 5k - 14 )

-112k - 140 = -3h + 5k - 14

3h - 112k - 5k = -14 + 140

3h - 117k = 126 . . . (2)

By solving equation (1) × 13 and equation (2) .

h = 3

By putting the value of h in equation (1) , we get

K = -1 .

Therefore, the coordinates are (3, -1) .

Hence, the correct option is (a).

The equation of the circle is 2x

^{2}+ 2y^{2}- 3x + 5y - 7 = 0.Dividing both sides of the equation by 2,we get

x

^{2}+ y^{2}- 3/2 x + 5/2 y - 7/2 = 0.The equation of polar for the point having coordinates (h, k) is

h x + k y - 3/4 (x + h) + 5/4 (y+k) - 7/2 = 0 .

Simplifying the equation, it can be written as (4h - 3)x + (4k + 5)y + (-3h + 5k - 14).

We are given that the equation of the polar is 9x + y - 28 = 0.so, the above equation and this equation represent the same line. Comparing the coefficient of the line, we get

(4h - 3) /9 = (4k + 5) /1 = (-3h + 5k - 14) /-28

Taking the first and third expression, we get

(4h - 3) /9 = (-3h + 5k - 14) /-28 .

By cross multiplication, we get

Or, -28 (4h - 3) = 9 (-3h + 5k - 14)

Or, -112h + 84 = -27h + 45k - 126

Or, -112h + 27h - 45k = -126 - 84

Or, -85h - 45k = -210

Or, -5 ( 17h + 9k ) = -210

17h + 9k = 42 . . . (1)

Taking the second and third expression, we get

(4k + 5) /1 = ( -3h + 5k - 14) /-28

By cross multiplication, we get

-28 ( 4k + 5 ) = ( -3h + 5k - 14 )

-112k - 140 = -3h + 5k - 14

3h - 112k - 5k = -14 + 140

3h - 117k = 126 . . . (2)

By solving equation (1) × 13 and equation (2) .

h = 3

By putting the value of h in equation (1) , we get

K = -1 .

Therefore, the coordinates are (3, -1) .

Hence, the correct option is (a).

physics-

### Three rods of equal length are joined to form an equilateral triangle O is the mid point of Distance remains same for small change in temperature. Coefficient of linear expansion for and is same, but that for is Then

Neglecting and

### Three rods of equal length are joined to form an equilateral triangle O is the mid point of Distance remains same for small change in temperature. Coefficient of linear expansion for and is same, but that for is Then

physics-General

Neglecting and

physics-

### A point source causes photoelectric effect from a small metal plate Which of the following curves may represent the saturation photocurrent as a function of the distance between the source and the metal?

### A point source causes photoelectric effect from a small metal plate Which of the following curves may represent the saturation photocurrent as a function of the distance between the source and the metal?

physics-General

physics-

### One of the following figures respesents the variation of particle momentum with associated de Broglie wavelength

a)

b)

c)

### One of the following figures respesents the variation of particle momentum with associated de Broglie wavelength

a)

b)

c)

physics-General

physics-

### Two circular discs A and B with equal radii are blackened. They are heated to some temperature and are cooled under identical conditions. What inference do you draw from their cooling curves?

According to Newton’s law of cooling, rate of cooling is given by

Where c is specific heat of material.

or

rate of cooling varies inversely as specific heat. From the graph, for A rate of cooling is larger. Therefore, specific heat of A is smaller.

Where c is specific heat of material.

or

rate of cooling varies inversely as specific heat. From the graph, for A rate of cooling is larger. Therefore, specific heat of A is smaller.

### Two circular discs A and B with equal radii are blackened. They are heated to some temperature and are cooled under identical conditions. What inference do you draw from their cooling curves?

physics-General

According to Newton’s law of cooling, rate of cooling is given by

Where c is specific heat of material.

or

rate of cooling varies inversely as specific heat. From the graph, for A rate of cooling is larger. Therefore, specific heat of A is smaller.

Where c is specific heat of material.

or

rate of cooling varies inversely as specific heat. From the graph, for A rate of cooling is larger. Therefore, specific heat of A is smaller.

physics-

### Which of the curves in figure represents the relation between Celsius and Fahrenheit temperatures

Hence graph between and will be a straight line with positive slope and negative intercept

### Which of the curves in figure represents the relation between Celsius and Fahrenheit temperatures

physics-General

Hence graph between and will be a straight line with positive slope and negative intercept