Conic Sections Question 170
Question: The equation of the normal to the ellipse $ \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 $ at the point $ (a\cos \theta ,\ b\sin \theta ) $ is
Options:
A) $ \frac{ax}{\sin \theta }-\frac{by}{\cos \theta }=a^{2}-b^{2} $
B) $ \frac{ax}{\sin \theta }-\frac{by}{\cos \theta }=a^{2}+b^{2} $
C) $ \frac{ax}{\cos \theta }-\frac{by}{\sin \theta }=a^{2}-b^{2} $
D) $ \frac{ax}{\cos \theta }-\frac{by}{\sin \theta }=a^{2}+b^{2} $
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Answer:
Correct Answer: C
Solution:
$ ax\sec \theta -by\text{ cosec}\theta =a^{2}-b^{2} $ . (See theory for formula of tangent on ellipse at parametric point)
BETA
