Question

The pole of the line $9x+2y=1$ with respect to the ellipse $3x^2+2y^2=1$ is:

• A. $(3,1)$
• B. $(4,1)$
• C. $(3,2)$
• D. $(1,3)$

Answer 1

The correct option is A $(3,1)$

Pole of the line $9x+2y=1$ w.r.t ${3x}^2+{2y}^2=1$

Let $(x_1,y_1)$ be pole of ellipse,

Then polar of $(x_1,y_1)$$=\frac{{xx}_1}{\frac{1}{3}}+\frac{{yy}_1}{\frac{1}{2}}=1⟶\left(2\right)$

and (2) will be equal to line $9x+2y=1$

Comparing coefficients,

$\frac{x_1}{\frac{1}{3}\times 9}=\frac{y_1}{\frac{1}{2}\times 2}=\frac{1}{1}$

$x_1=3,y_1=1$

OR

(3,1) is the pole of line $9x+2y=1$ w.r.t ${3x}^2+{2y}^2=1$