Question:
The image of the point $(3, 4)$ with respect to the radical axis of the circles $x^2 + y^2 + 8x + 2y + 10 = 0$ and $x^2 + y^2 + 7x + 3y + 10 = 0$ is
The image of the point $(3, 4)$ with respect to the radical axis of the circles $x^2 + y^2 + 8x + 2y + 10 = 0$ and $x^2 + y^2 + 7x + 3y + 10 = 0$ is
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To reflect across $x = y$, simply swap coordinates.
Updated On: May 19, 2025
- $(3, 4)$
- $(-4, -3)$
- $(4, 3)$
- $(3, -4)$
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The Correct Option is C
Solution and Explanation
Find radical axis: Subtract equations
$(x^2 + y^2 + 8x + 2y + 10) - (x^2 + y^2 + 7x + 3y + 10)$
$\Rightarrow x + (-y) = 0 \Rightarrow x = y$
Image of $(3,4)$ reflected across $x = y$ is $(4,3)$
$(x^2 + y^2 + 8x + 2y + 10) - (x^2 + y^2 + 7x + 3y + 10)$
$\Rightarrow x + (-y) = 0 \Rightarrow x = y$
Image of $(3,4)$ reflected across $x = y$ is $(4,3)$
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