Question

If a tangent to the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$, whose centre is C, meets the major and minor axes at P and Q respectively, then $\frac{a^{2}}{CP^{2}} + \frac{b^{2}}{CQ^{2}}$ is equal to

• A. a² + b²
• B. a² - b²
• C. $\sqrt{2}$
• D. 1

Answer 1

Answer: (D)

1

Answer 2

Equation of tangent is y = mx + $\sqrt{a^{2}m^{2} + b^{2}}$.

At x = 0; CQ = $\sqrt{a^{2}m^{2} + b^{2}}$

At y = 0; CP = $- \frac{\sqrt{a^{2}m^{2} + b^{2}}}{m}$

∴ $\frac{a^{2}}{CP^{2}} + \frac{b^{2}}{CQ^{2}} = \frac{a^{2}m^{2}}{a^{2}m^{2} + b^{2}} + \frac{b^{2}}{a^{2}m^{2} + b^{2}} = 1$.