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Maths-

General

Easy

Question

P(θ) and $D space open parentheses theta plus pi over 2 close parentheses$ are the pts. on the ellipse $b x to the power of 2 end exponent plus a to the power of 2 end exponent y to the power of 2 end exponent equals a to the power of 2 end exponent b to the power of 2 end exponent$ then $C P to the power of 2 end exponent plus C D to the power of 2 end exponent equals$

ab
a+b
$a^{2} - b^{2}$
$a^{2} + b^{2}$

hint Hint:

With the help of equation of ellipse and distance formula, find the answer. Take centre as $open parentheses 0 comma 0 close parentheses$

The correct answer is: a+b

$L e t space x squared over a squared plus y squared over b squared equals 1 space b e space a n space e l l i p s e C e n t r e space i s space g i v e n space a s space C open parentheses 0 comma 0 close parentheses L e t P open parentheses theta close parentheses equals open parentheses a cos theta comma b sin theta close parentheses D open parentheses theta plus straight pi over 2 close parentheses equals open parentheses a cos open parentheses theta plus straight pi over 2 close parentheses comma b sin open parentheses theta plus straight pi over 2 close parentheses close parentheses equals open parentheses negative a sin theta comma b cos theta close parentheses B y space d i s tan c e space f o r m u l a comma C P squared equals open parentheses open parentheses a cos theta close parentheses squared plus open parentheses b sin theta close parentheses squared close parentheses equals a squared cos squared theta plus b squared sin squared theta C D squared equals open parentheses open parentheses negative a sin theta close parentheses squared plus open parentheses b c o s theta close parentheses squared close parentheses equals a squared sin squared theta plus b squared cos squared theta rightwards double arrow C P squared plus C D squared equals a squared cos squared theta plus b squared sin squared theta plus a squared sin squared theta plus b squared cos squared theta equals a squared open parentheses cos squared theta plus sin squared theta close parentheses plus b squared open parentheses sin squared theta plus cos squared theta close parentheses equals a squared plus b squared$

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