Question

If the tangent at point P on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ meets the major axis at T, C is the centre and PN is the perpendicular on major axis, then the value of CN.CT is

• A. $a^2$
• B. $b^2$
• C. $2a^2$
• D. $2b^2$

Answer 1

The correct option is A $a^2$

Equation of tangent at P is $\frac{x}{a}\cos \theta +\frac{y}{b}\sin \theta =1$
$T=(\frac{a}{\cos \theta },0);CN=a\cos \theta .$
$\therefore CT.CN=\frac{a}{\cos \theta }.a\cos \theta =a^2$