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If p(theta) is a point on the ellipse ...

If `p(theta)` is a point on the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (agtb)` then find its coresponding point

Text Solution

Verified by Experts

The correct Answer is:
`(a cos theta,a sin theta)`
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Knowledge Check

  • If the normal at a point P on the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1, (a gt b) meets the axes in M and N, then (PM)/(PN)=

    A
    `1-e^(2)`
    B
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    C
    `1+e^(2)`
    D
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  • P is a point on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 S and S^(1) are foci A & A^(1) are the vertices of the ellipse then the ratio |(SP-S^(1)P)/(SP+S^(1)P)| is

    A
    e cos `theta`
    B
    `e^(2) cos theta`
    C
    `e^(3) cos theta`
    D
    `(1)/(e ) cos theta`

  • Assertion (A) If the tangent and normal to the ellipse 9x^(2)+16y^(2)=144 at the point P(pi/3) on it meet the major axis in Q and R respectively, then QR=(57)/(8) . Reason (R) If the tangent and normal to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))= at the point P(theta) on it meet the major axis in Q and R respectively, then QR=|(a^(2)sin^(2)theta-b^(2)cos^(2)theta)/(a cos theta)| The correct answer is

    A
    Both (A) and (R) are true and (R) is the correct explanation of (A).
    B
    Both (A) and (R) are true but (R) is not the correct explanation of (A).
    C
    (A) is true but (R) is false.
    D
    (A) is false but (R) is true.

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