Question

The pole of the straight line \[ 9x + y - 28 = 0 \] with respect to the circle \[ 2x^2 + 2y^2 - 3x + 5y - 7 = 0 \] is:

• A. \( (-1,3) \)
• B. \( (2,-3) \)
• C. \( (3,-1) \)
• D. \( (3,-3) \)

Hint:

The pole of a line with respect to a circle can be found using the general pole formula based on the equation of the given conic.

Answer 1

The Correct Option is C

Step 1: Finding the pole of the line with respect to the given circle The equation of the given circle is: \[ 2x^2 + 2y^2 - 3x + 5y - 7 = 0. \] To find the pole of the line \( 9x + y - 28 = 0 \), we use the pole formula: \[ X = - \frac{A_1 C_1 + B_1 D_1}{A_1^2 + B_1^2}, \quad Y = - \frac{B_1 C_1 - A_1 D_1}{A_1^2 + B_1^2}. \] After solving, we get the coordinates of the pole as \( (3,-1) \).