Home
Class 12
MATHS
Consider an ellipse x^2/25+y^2/16=1. A c...

Consider an ellipse `x^2/25+y^2/16=1`. A circle passes through a focus and has its centre on `y= 0` and touches the ellipse at A and S is focus, then

A

`[|AS|]` is less than 7

B

`|AS|lt4`

C

`5lt|AS|lt6`

D

`|AS|gt4`

Text Solution

Verified by Experts

The correct Answer is:
A, D
Using property and simplifying
Promotional Banner

Similar Questions

Explore conceptually related problems

A circle passes through (0,0) and (1, 0) and touches the circle x^2 + y^2 = 9 then the centre of circle is -

A variable circle passes through the fixed point (2, 0) and touches y-axis Then, the locus of its centre, is

A variable circle passes through the fixed point (2, 0) and touches y-axis Then, the locus of its centre, is

If a hyperbola passes through the foci of the ellipse (x^2)/(25)+(y^2)/(16)=1 . Its transverse and conjugate axes coincide respectively with the major and minor axes of the ellipse and if the product of eccentricities of hyperbola and ellipse is 1 then the equation of a. hyperbola is (x^2)/9-(y^2)/(16)=1 b. the equation of hyperbola is (x^2)/9-(y^2)/(25)=1 c. focus of hyperbola is (5, 0) d. focus of hyperbola is (5sqrt(3),0)

If a hyperbola passes through the foci of the ellipse (x^2)/(25)+(y^2)/(16)=1 . Its transverse and conjugate axes coincide respectively with the major and minor axes of the ellipse and if the product of eccentricities of hyperbola and ellipse is 1 then the equation of hyperbola is (x^2)/9-(y^2)/(16)=1 b. the equation of hyperbola is (x^2)/9-(y^2)/(25)=1 c. focus of hyperbola is (5, 0) d. focus of hyperbola is (5sqrt(3),0)

If a hyperbola passes through the foci of the ellipse (x^2)/(25)+(y^2)/(16)=1 . Its transverse and conjugate axes coincide respectively with the major and minor axes of the ellipse and if the product of eccentricities of hyperbola and ellipse is 1 then the equation of a. hyperbola is (x^2)/9-(y^2)/(16)=1 b. the equation of hyperbola is (x^2)/9-(y^2)/(25)=1 c. focus of hyperbola is (5, 0) d. focus of hyperbola is (5sqrt(3),0)

let the eccentricity of the hyperbola x^2/a^2-y^2/b^2=1 be reciprocal to that of the ellipse x^2+4y^2=4. if the hyperbola passes through a focus of the ellipse then: (a) the equation of the hyperbola is x^2/3-y^2/2=1 (b) a focus of the hyperbola is (2,0) (c) the eccentricity of the hyperbola is sqrt(5/3) (d) the equation of the hyperbola is x^2-3y^2=3

A parabola is drawn whose focus is one of the foci of the ellipse x^2/a^2 + y^2/b^2 = 1 (where a>b) and whose directrix passes through the other focus and perpendicular to the major axes of the ellipse. Then the eccentricity of the ellipse for which the length of latus-rectum of the ellipse and the parabola are same is

Column I, Column II An ellipse passing through the origin has its foci (3, 4) and (6,8). Then the length of its minor axis is, p. 8 If P Q is a focal chord of the ellipse (x^2)/(25)+(y^2)/(16)=1 which passes through S-=(3,0) and P S=2, then the length of chord P Q is, q. 10sqrt(2) If the line y=x+K touches the ellipse 9x^2+16 y^2=144 , then the difference of values of K is, r. 10 The sum of distances of a point on the ellipse (x^2)/9+(y^2)/(16)=1 from the foci is, s. 12

An ellipse passes through the point (2,3) and its axes along the coordinate axes, 3x +2y -1 = 0 is a tangent to the ellipse, then the equation of the ellipse is