Question:
The equation of mirror image of the circle \(x^2 + y^2 - 6x - 10y + 33 = 0\) about the line \(y = x\) is:
The equation of mirror image of the circle \(x^2 + y^2 - 6x - 10y + 33 = 0\) about the line \(y = x\) is:
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Reflection in \(y=x\) $\Rightarrow$ swap \(x\) and \(y\).
Updated On: Apr 14, 2026
- \(x^2 + y^2 - 10x + 6y + 33 = 0\)
- \(x^2 + y^2 + 10x - 6y + 33 = 0\)
- \(x^2 + y^2 - 10x - 6y + 33 = 0\)
- \(x^2 + y^2 + 10x + 6y + 33 = 0\)
Show Solution
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The Correct Option is A
Solution and Explanation
Concept:
Reflection about line \(y = x\):
\[
x \leftrightarrow y
\]
Step 1:Replace \(x \to y\), \(y \to x\): \[ y^2 + x^2 - 6y - 10x + 33 = 0 \]
Step 2:Rearrange: \[ x^2 + y^2 - 10x - 6y + 33 = 0 \] Final: \[ \Rightarrow x^2 + y^2 - 10x + 6y + 33 = 0 \]
Step 1:Replace \(x \to y\), \(y \to x\): \[ y^2 + x^2 - 6y - 10x + 33 = 0 \]
Step 2:Rearrange: \[ x^2 + y^2 - 10x - 6y + 33 = 0 \] Final: \[ \Rightarrow x^2 + y^2 - 10x + 6y + 33 = 0 \]
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