Question

# If the equation represents a pair of straight lines then their point of intersection is

- (-3, -1)
- (-1, -3)
- (3,1)
- (1,3)

Hint:

### First find the value of coefficient of x square and then find the point of intersection.

## The correct answer is: (-3, -1)

### Given That:

If the equation represents a pair of straight lines then their point of intersection is

>>> λx^{2} – 5xy + 6y^{2} + x – 3y = 0

>>> Comparing with general equation, ax^{2} + 2hxy + by^{2} + 2gx + 2fy + c = 0

We get a = λ, h = -5/2, b = 6, g = 1/2, f = -3/2, c = 0

>>> The condition for straight lines is abc + 2fgh – af2 – bg2 – ch2 = 0

=> λ×6×0 + 2×-3/2×1/2×-5/2 – λ×9/4 – 6×1/4 – 0 = 0

=> 0 + 15/4 – 9λ/4 – 3/2 = 0

=> 9/4 = 9λ/4

=> λ = 1

>>>> So the equation becomes x^{2} – 5xy + 6y^{2} + x – 3y = 0

=> x^{2} – 3xy – 2xy + 6y^{2} + x – 3y = 0

=> x(x – 3y) – 2y(x – 3y) + x – 3y =0

=> (x – 3y)(x – 2y + 1) = 0

So x – 3y = 0 …(i)

x – 2y + 1 = 0 ..(ii)

Solving (i) and (ii)

We get x = -3, y = -1

>>>The point of intersection of the pair of straight lines x^{2} – 5xy + 6y^{2} + x – 3y = 0 is (-3, -1)

>>>The point of intersection of the pair of straight lines x^{2} – 5xy + 6y^{2} + x – 3y = 0 is (-3, -1)

### Related Questions to study

### The point of intersection of the perpendicular lines is

### The point of intersection of the perpendicular lines is

### In the structure the configurations at chiral centers are:

### In the structure the configurations at chiral centers are:

### Which of the following compound are meso forms?

### Which of the following compound are meso forms?

### The number of enantiomers of the compound is:

### The number of enantiomers of the compound is:

### Following stereo-structure of tartaric acid represents:

### Following stereo-structure of tartaric acid represents:

### The transformed equation of when the axes are rotated through an angle 36° is

## >>> Given equation is $x2+y2=r2.$ After rotation

## $>>> x=Xcos36_{∘}−Ysin36_{∘}$and $y=Xsin36_{o}+Ycos36_{∘}$

## $∴X2(cos_{2}36_{o}+sin_{2}36_{o})+Y2(sin_{2}36_{o}+cos_{2}36_{o})=r2$

## $>>> ⇒X2+Y2=r2$

### The transformed equation of when the axes are rotated through an angle 36° is

## >>> Given equation is $x2+y2=r2.$ After rotation

## $>>> x=Xcos36_{∘}−Ysin36_{∘}$and $y=Xsin36_{o}+Ycos36_{∘}$

## $∴X2(cos_{2}36_{o}+sin_{2}36_{o})+Y2(sin_{2}36_{o}+cos_{2}36_{o})=r2$

## $>>> ⇒X2+Y2=r2$

### When axes rotated an angle of the transformed form of is

### When axes rotated an angle of the transformed form of is

### The transformed equation of when the axes are rotated through an angle 90° is

>>> Therefore, the equation becomes =1.

### The transformed equation of when the axes are rotated through an angle 90° is

>>> Therefore, the equation becomes =1.

### The arrangement of the following in ascending order of angle to eliminate xy term in the following equations

A)

B)

C)

### The arrangement of the following in ascending order of angle to eliminate xy term in the following equations

A)

B)

C)

### The angle of rotation of axes to remove xy term of the equation is

## Angle of rotation will be $45 degrees.$

### The angle of rotation of axes to remove xy term of the equation is

## Angle of rotation will be $45 degrees.$

### The angle of rotation of axes in order to eliminate xy term of the equation is

The Angle of rotation becomes

### The angle of rotation of axes in order to eliminate xy term of the equation is

The Angle of rotation becomes

### If the axes are rotated through an angle 45° in the anti-clockwise direction, the coordinates of in the new system are

The point () becomes (2,0) after rotation through 45 degrees in anti clockwise direction.

### If the axes are rotated through an angle 45° in the anti-clockwise direction, the coordinates of in the new system are

The point () becomes (2,0) after rotation through 45 degrees in anti clockwise direction.

### If the axes are rotated through an angle of 45° and the point p has new co-ordinates then original coordinates of p are

>>> Therefore, the original point is (3,1).

### If the axes are rotated through an angle of 45° and the point p has new co-ordinates then original coordinates of p are

>>> Therefore, the original point is (3,1).

### Assertion (A) : If the area of triangle formed by (0,0),(-1,2),(1,2) is 2 square units. Then the area triangle on shifting the origin to a point (2,3) is 2 units.

Reason (R):By the change of axes area does not change

Choose the correct answer

Both assertion and reason are correct and the reason is correct explanation of assertion.

### Assertion (A) : If the area of triangle formed by (0,0),(-1,2),(1,2) is 2 square units. Then the area triangle on shifting the origin to a point (2,3) is 2 units.

Reason (R):By the change of axes area does not change

Choose the correct answer

Both assertion and reason are correct and the reason is correct explanation of assertion.

### The point (4,1) undergoes the following successively

i) reflection about the line y=x

ii) translation through a distance 2 unit along the positive direction of y-axis. The final position of the point is

Therefore, the required point is (1,6).

### The point (4,1) undergoes the following successively

i) reflection about the line y=x

ii) translation through a distance 2 unit along the positive direction of y-axis. The final position of the point is

Therefore, the required point is (1,6).