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The normal at a point `P` on the ellipse `x^2+4y^2=16` meets the x-axis at `Qdot` If `M` is the midpoint of the line segment `P Q ,` then the locus of `M` intersects the latus rectums of the given ellipse at points. `(+-((3sqrt(5)))/2+-2/7)` (b) `(+-((3sqrt(5)))/2+-(sqrt(19))/7)` `(+-2sqrt(3),+-1/7)` (d) `(+-2sqrt(3)+-(4sqrt(3))/7)`

A

`(pm(3sqrt5/2,pm2/7)`

B

`(pm(3sqrt5/2,pmsqrt19/4)`

C

`(pm2sqrt3,pm1/7)`

D

`(pm2sqrt3,pm(4sqrt3/7)`

Text Solution

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The correct Answer is:
C
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The normal at a point P on the ellipse x^2+4y^2=16 meets the x-axis at Qdot If M is the midpoint of the line segment P Q , then the locus of M intersects the latus rectums of the given ellipse at points. (a)(+-((3sqrt(5)))/2+-2/7) (b) (+-((3sqrt(5)))/2+-(sqrt(19))/7) (c)(+-2sqrt(3),+-1/7) (d) (+-2sqrt(3)+-(4sqrt(3))/7)

(2sqrt(7))/(sqrt(5)-sqrt(3))

(sqrt(3)-sqrt(5))(sqrt(3)+sqrt(5))/(sqrt(7)-2sqrt(5))

(1)/(sqrt(11-2sqrt(30)))-(3)/(sqrt(7-2sqrt(10)))-(4)/(sqrt(8+4sqrt(3)))

The eccentricity of the ellipse 4x^(2)+9y^(2)=36 is (1)/(2sqrt(3)) b.(1)/(sqrt(3)) c.(sqrt(5))/(3) d.(sqrt(5))/(6)

tan^(2)((1)/(2)sin^(-1)(2)/(3))= (A) (7+3sqrt(3))/(2) (B) (7-5sqrt(3))/(2) (C) (7-3sqrt(5))/(2) (D) (7+5sqrt(3))/(2)

(5+2sqrt(3))/(7+4sqrt(3))=a-b sqrt(3)

(5+2sqrt(3))/(7+4sqrt(3))=a-b sqrt(3)

Simplify: (7+3sqrt(5))/(3+sqrt(5))-(7-3sqrt(5))/(3-sqrt(5)) (ii) (1)/(2+sqrt(3))+(2)/(sqrt(5)-sqrt(3))+(1)/(2-sqrt(5))

ARIHANT MATHS-ELLIPSE-Exercise (Questions Asked In Previous 13 Years Exam)
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  12. Statement 1: An equation of a common tangent to the parabola y^2=16...

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  17. Tangents are drawn to the ellipse x^2/9+y^2/5 = 1 at the end of latus ...

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  18. Let E1 and E2, be two ellipses whose centers are at the origin.The maj...

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  19. Suppose that the foci of the ellipse (x^2)/9+(y^2)/5=1 are (f1,0)a n d...

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