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Let P be any point on any directrix of an ellipse Then the chords of contact of point P with respect to the ellipse and its auxiliary circle intersect at

some point on the major axis depending upon the position of point P
the midpoint of the line segment joining the center to the corresponding focus
the corresponding focus
none of these

The correct answer is: the corresponding focus

Given that Let P be any point on any directrix of an ellipse Then we need to find the chords of contact of point P with respect to the ellipse and its auxiliary circle intersect at what point
$L e t space e l l i p s e space i s fraction numerator space x squared space space space over denominator a squared end fraction plus space space y squared over b squared space space space equals 1 space w h e r e space a greater than b greater than 0 space a n d space p o i n t space P space i s left parenthesis space a over e space comma k right parenthesis A u x i l i a r y space c i r c l e space i s space x squared plus y squared space equals a squared space space C h o r d s space o f space c o n t a c t space a r e fraction numerator space x a over denominator e a squared end fraction plus fraction numerator y k over denominator b squared end fraction equals 1 space a n d fraction numerator space x a over denominator e end fraction plus y k equals a squared space space open parentheses fraction numerator space x over denominator a e end fraction minus 1 close parentheses plus k open parentheses y over b squared close parentheses equals 0 space a n d space open parentheses fraction numerator space x a over denominator e end fraction minus a squared close parentheses equals plus k y equals 0$
which are family of concurrent lines passing through point $(a e, 0)$ i.e. focus of ellipse

Therefore, the chords of contact of point P with respect to the ellipse and its auxiliary circle intersect at the corresponding focus.

An ellipse having foci at (3, 3) and (-4,4) and passing through the origin has eccentricity equal to‐

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Normals $A O comma A A subscript 1 end subscript comma A A subscript 2 end subscript$ are drawn to parabola $y to the power of 2 end exponent equals 8 x$ from the pointA (h, 0) If triangle $O A subscript 1 end subscript A subscript 2 end subscript$ ( $O$ being the origin) is equilateral, then possible value of h’ is

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maths-

Given: A circle, $2 x to the power of 2 end exponent plus 2 y to the power of 2 end exponent equals 5$ and a parabola, $y to the power of 2 end exponent equals 4 square root of 5 x$
Statement‐I:: An equation of a common tangent to these curves is $y equals x plus square root of 5.$
Statement‐II:: If the line, $y equals m x plus fraction numerator square root of 5 over denominator m end fraction left parenthesis m not equal to 0 right parenthesis$ is their common tangent, then $m$ satisfies $m to the power of 4 end exponent minus 3 m to the power of 2 end exponent plus 2 equals 0.$

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maths-

In any equilateral $capital delta$ , three circles of radii one are touching to the sides given as in the figure then area of the $capital delta$ is

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maths-

If the sides a, b, c of a triangle are such that a : b : c : : 1 : $square root of 3$ : 2, then the A : B : C is -

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physics-

A block placed on a rough inclined plane of inclination ( $theta$ =30°) can just be pushed upwards by applying a force "F" as shown. If the angle of inclination of the inclined plane is increased to ( $theta$ = 60°), the same block can just be prevented from sliding down by application of a force of same magnitude. The coefficient of friction between the block and the inclined plane is

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physics-

The tube AC forms a quarter circle in a vertical plane. The ball B has an area of cross–section slightly smaller than that of the tube, and can move without friction through it. B is placed at A and displaced slightly. It will

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physics-

A small cube with mass M starts at rest at point 1 at a height 4R, where R is the radius of the circular part of the track. The cube slides down the frictionless track and around the loop. The force that the track exerts on the cube at point 2 is nearly _____ times the cube's weight Mg.

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physics-

A bob attached to a string is held horizontal and released. The tension and vertical distance from point of suspension can be represented by.

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physics-

A ball whose size is slightly smaller than width of the tube of radius 2.5 m is projected from bottommost point of a smooth tube fixed in a vertical plane with velocity of 10 m/s. If N₁ and N₂ are the normal reactions exerted by inner side and outer side of the tube on the ball

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A block of mass m moving with a velocity v₀ on a smooth horizontal surface strikes and compresses a spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
A: standing on the horizontal surface
B: standing on the block

According to observer B, the potential energy of the spring increases

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physics-

A block of mass m moving with a velocity v0 on a smooth horizontal surface strikes and compresses a spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
A: standing on the horizontal surface
B: standing on the block

To an observer B, when the block is compressing the spring

physics-General

General

physics-

A block of mass m moving with a velocity v₀ on a smooth horizontal surface strikes and compresses a spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
A: standing on the horizontal surface
B: standing on the block

According to the observer A

physics-General

General

physics-

A block of mass m moving with a velocity v0 on a smooth horizontal surface strikes and compresses a spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
A: standing on the horizontal surface
B: standing on the block

To an observer A, the net work done on the block is

physics-General

General

physics-

A block of mass m moving with a velocity v0 on a smooth horizontal surface strikes and compresses a spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
A: standing on the horizontal surface
B: standing on the block

To an observer A, the work done by the normal reaction N between the block and the spring on the block is

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Let P be any point on any directrix of an ellipse Then the chords of contact of point P with respect to the ellipse and its auxiliary circle intersect at

some point on the major axis depending upon the position of point P
the midpoint of the line segment joining the center to the corresponding focus
the corresponding focus
none of these

The correct answer is: the corresponding focus

Related Questions to study

An ellipse having foci at (3, 3) and (-4,4) and passing through the origin has eccentricity equal to‐

An ellipse having foci at (3, 3) and (-4,4) and passing through the origin has eccentricity equal to‐

In any equilateral $capital delta$ , three circles of radii one are touching to the sides given as in the figure then area of the $capital delta$ is

In any equilateral $capital delta$ , three circles of radii one are touching to the sides given as in the figure then area of the $capital delta$ is

If the sides a, b, c of a triangle are such that a : b : c : : 1 : $square root of 3$ : 2, then the A : B : C is -

If the sides a, b, c of a triangle are such that a : b : c : : 1 : $square root of 3$ : 2, then the A : B : C is -

The tube AC forms a quarter circle in a vertical plane. The ball B has an area of cross–section slightly smaller than that of the tube, and can move without friction through it. B is placed at A and displaced slightly. It will

The tube AC forms a quarter circle in a vertical plane. The ball B has an area of cross–section slightly smaller than that of the tube, and can move without friction through it. B is placed at A and displaced slightly. It will

A small cube with mass M starts at rest at point 1 at a height 4R, where R is the radius of the circular part of the track. The cube slides down the frictionless track and around the loop. The force that the track exerts on the cube at point 2 is nearly _____ times the cube's weight Mg.

A small cube with mass M starts at rest at point 1 at a height 4R, where R is the radius of the circular part of the track. The cube slides down the frictionless track and around the loop. The force that the track exerts on the cube at point 2 is nearly _____ times the cube's weight Mg.

A bob attached to a string is held horizontal and released. The tension and vertical distance from point of suspension can be represented by.

A bob attached to a string is held horizontal and released. The tension and vertical distance from point of suspension can be represented by.

A ball whose size is slightly smaller than width of the tube of radius 2.5 m is projected from bottommost point of a smooth tube fixed in a vertical plane with velocity of 10 m/s. If N₁ and N₂ are the normal reactions exerted by inner side and outer side of the tube on the ball

A ball whose size is slightly smaller than width of the tube of radius 2.5 m is projected from bottommost point of a smooth tube fixed in a vertical plane with velocity of 10 m/s. If N₁ and N₂ are the normal reactions exerted by inner side and outer side of the tube on the ball

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Let P be any point on any directrix of an ellipse Then the chords of contact of point P with respect to the ellipse and its auxiliary circle intersect at

some point on the major axis depending upon the position of point P the midpoint of the line segment joining the center to the corresponding focus the corresponding focus none of these

The correct answer is: the corresponding focus

Given that Let P be any point on any directrix of an ellipse Then we need to find the chords of contact of point P with respect to the ellipse and its auxiliary circle intersect at what pointwhich are family of concurrent lines passing through point (ae,0) i.e. focus of ellipse

Related Questions to study

An ellipse having foci at (3, 3) and (-4,4) and passing through the origin has eccentricity equal to‐

An ellipse having foci at (3, 3) and (-4,4) and passing through the origin has eccentricity equal to‐

Normals are drawn to parabola from the pointA (h, 0) If triangle ( being the origin) is equilateral, then possible value of h’ is

Normals are drawn to parabola from the pointA (h, 0) If triangle ( being the origin) is equilateral, then possible value of h’ is

Given: A circle, and a parabola, Statement‐I:: An equation of a common tangent to these curves is Statement‐II:: If the line, is their common tangent, then satisfies

Given: A circle, and a parabola, Statement‐I:: An equation of a common tangent to these curves is Statement‐II:: If the line, is their common tangent, then satisfies

In any equilateral , three circles of radii one are touching to the sides given as in the figure then area of the is

In any equilateral , three circles of radii one are touching to the sides given as in the figure then area of the is

If the sides a, b, c of a triangle are such that a : b : c : : 1 : : 2, then the A : B : C is -

If the sides a, b, c of a triangle are such that a : b : c : : 1 : : 2, then the A : B : C is -

The tube AC forms a quarter circle in a vertical plane. The ball B has an area of cross–section slightly smaller than that of the tube, and can move without friction through it. B is placed at A and displaced slightly. It will

The tube AC forms a quarter circle in a vertical plane. The ball B has an area of cross–section slightly smaller than that of the tube, and can move without friction through it. B is placed at A and displaced slightly. It will

A small cube with mass M starts at rest at point 1 at a height 4R, where R is the radius of the circular part of the track. The cube slides down the frictionless track and around the loop. The force that the track exerts on the cube at point 2 is nearly _____ times the cube's weight Mg.

A small cube with mass M starts at rest at point 1 at a height 4R, where R is the radius of the circular part of the track. The cube slides down the frictionless track and around the loop. The force that the track exerts on the cube at point 2 is nearly _____ times the cube's weight Mg.

A bob attached to a string is held horizontal and released. The tension and vertical distance from point of suspension can be represented by.

A bob attached to a string is held horizontal and released. The tension and vertical distance from point of suspension can be represented by.

A ball whose size is slightly smaller than width of the tube of radius 2.5 m is projected from bottommost point of a smooth tube fixed in a vertical plane with velocity of 10 m/s. If N1 and N2 are the normal reactions exerted by inner side and outer side of the tube on the ball

A ball whose size is slightly smaller than width of the tube of radius 2.5 m is projected from bottommost point of a smooth tube fixed in a vertical plane with velocity of 10 m/s. If N1 and N2 are the normal reactions exerted by inner side and outer side of the tube on the ball

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some point on the major axis depending upon the position of point P
the midpoint of the line segment joining the center to the corresponding focus
the corresponding focus
none of these

In any equilateral $capital delta$ , three circles of radii one are touching to the sides given as in the figure then area of the $capital delta$ is

In any equilateral $capital delta$ , three circles of radii one are touching to the sides given as in the figure then area of the $capital delta$ is

If the sides a, b, c of a triangle are such that a : b : c : : 1 : $square root of 3$ : 2, then the A : B : C is -

If the sides a, b, c of a triangle are such that a : b : c : : 1 : $square root of 3$ : 2, then the A : B : C is -

A ball whose size is slightly smaller than width of the tube of radius 2.5 m is projected from bottommost point of a smooth tube fixed in a vertical plane with velocity of 10 m/s. If N₁ and N₂ are the normal reactions exerted by inner side and outer side of the tube on the ball

A ball whose size is slightly smaller than width of the tube of radius 2.5 m is projected from bottommost point of a smooth tube fixed in a vertical plane with velocity of 10 m/s. If N₁ and N₂ are the normal reactions exerted by inner side and outer side of the tube on the ball