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If the normal at the point P(theta) to t...

If the normal at the point `P(theta)` to the ellipse `x^2/14+y^2/5=1` intersects it again at the point `Q(2theta),` then `Costheta` is equal to (A) `2/3` (B) `(-2)/3` (C) `3/4` (D) non of these

Text Solution

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Co-ordinates at point `P(theta)` will be `(acostheta,bsintheta)`.
Co-ordinates at point `Q(2theta)` will be `(acos2theta,bsin2theta).`
Slope of joining these teo points will be,
`m_1 = (bsin2theta - bsintheta)/(acos2theta-acostheta)`
At any point, slope of normal can be given by
`m_2=a/btantheta`
As both slopes are on same line, they should be equal.
`:. (bsin2theta - bsintheta)/(acos2theta-acostheta) = a/btantheta`
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