Question

The pole of the line $\dfrac{x}{a} + \dfrac{y}{b} = 1$ with respect to the circle $x^2 + y^2 = c^2$ is

• A. $\left( \dfrac{c^2}{a}, \dfrac{c^2}{b} \right)$
• B. $\left( \dfrac{c^2}{b}, \dfrac{c^2}{a} \right)$
• C. $\left( \dfrac{c}{a}, \dfrac{c}{b} \right)$
• D. $\left( \dfrac{c}{b}, \dfrac{c}{a} \right)$

Hint:

Use the standard pole formula: Pole of $\dfrac{x}{a} + \dfrac{y}{b} = 1$ w.r.t. $x^2 + y^2 = c^2$ is $\left(\dfrac{c^2}{a}, \dfrac{c^2}{b}\right)$.

Answer 1

The Correct Option is A

The general formula for the pole of line $\dfrac{x}{a} + \dfrac{y}{b} = 1$ with respect to the circle $x^2 + y^2 = c^2$ is:
$\left( c^2 \cdot \dfrac{1}{a}, c^2 \cdot \dfrac{1}{b} \right) = \left( \dfrac{c^2}{a}, \dfrac{c^2}{b} \right)$