Conic Sections Question 483
Question: If $ 4x^{2}+py^{2}=45 $ and $ x^{2}-4y^{2}=5 $ cut orthogonally, then the value of p is
[Kerala (Engg.) 2005]
Options:
A) 1/9
B) 1/3
C) 3
D) 18
E) 9
Show Answer
Answer:
Correct Answer: E
Solution:
Slope of 1st curve $ {{( \frac{dy}{dx} )} _{I}}=-\frac{4x}{py} $
Slope of 2nd curve $ {{( \frac{dy}{dx} )} _{II}}=\frac{x}{4y} $
For orthogonal intersection $ ( -\frac{4x}{py} )( \frac{x}{4y} )=-1 $
therefore $ x^{2}=py^{2} $
On solving equations of given curves $ x=3 $ , $ y=1 $
$ p(1)={{(3)}^{2}}=9 $
therefore $ p=9 $ .
BETA
