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:
The pole of the straight line
\[
9x + y - 28 = 0
\]
with respect to the circle
\[
2x^2 + 2y^2 - 3x + 5y - 7 = 0
\]
is:
Show 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.
Updated On: Mar 24, 2025
- \( (-1,3) \)
- \( (2,-3) \)
- \( (3,-1) \)
- \( (3,-3) \)
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The Correct Option is C
Solution and Explanation
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 \( (3,-1) \).
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