Question:
The polar of a point with respect to the circle \( x^2 + y^2 - 10x + 12y - 3 = 0 \), which is not a tangent and not a chord of contact, is:
The polar of a point with respect to the circle \( x^2 + y^2 - 10x + 12y - 3 = 0 \), which is not a tangent and not a chord of contact, is:
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The polar of a point with respect to a circle is a straight line whose equation is derived from the equation of the circle by replacing \( x^2 \) with \( xx_1 \), \( y^2 \) with \( yy_1 \), and so on.
Updated On: May 15, 2025
- \( 2x + 3y + 8 = 0 \)
- \( 3x + 4y + 5 = 0 \)
- \( 5x - 12y + 7 = 0 \)
- \( 6x - 8y + 15 = 0 \)
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The Correct Option is D
Solution and Explanation
The given circle is:
\[
x^2 + y^2 - 10x + 12y - 3 = 0
\]
Let the point be \( (x_1, y_1) \). The equation of the polar is:
\[
xx_1 + yy_1 - 5(x + x_1) + 6(y + y_1) = 3
\]
The point is such that this line is neither a tangent nor a chord of contact. The given line \( 6x - 8y + 15 = 0 \) satisfies these conditions.
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