Conic Sections Question 361

Question: The distance of the point $ ‘\theta ’ $ on the ellipse $ \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 $ from a focus is

Options:

A) $ a(e+\cos \theta ) $

B) $ a(e-\cos \theta ) $

C) $ a(1+e\cos \theta ) $

D) $ a(1+2e\cos \theta ) $

Show Answer

Answer:

Correct Answer: C

Solution:

Focal distance of any point P (x,y) on the ellipse is equal to $ SP=a+ex $ . Here $ x=a\cos \theta $

Here $ SP=a+ae\cos \theta =a(1+e\cos \theta ) $ .