Question:
The circles
$$
x^2 + y^2 - 2x - 4y - 4 = 0
$$
and
$$
x^2 + y^2 + 2x + 4y - 11 = 0
$$
...
The circles
$$
x^2 + y^2 - 2x - 4y - 4 = 0
$$
and
$$
x^2 + y^2 + 2x + 4y - 11 = 0
$$
...
Show Hint
Radical axis represents locus of points with equal power to both circles.
Updated On: Jun 4, 2025
- Cut each other orthogonally
- Do not meet
- Intersect at points lying on the line \( 4x + 8y - 7 = 0 \)
- Touch each other at the point lying on the line \( 4x + 8y - 7 = 0 \)
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The Correct Option is C
Solution and Explanation
Centers: \[ C_1 = (1, 2), \quad C_2 = (-1, -2) \] Radii: \[ r_1 = \sqrt{1^2 + 2^2 + 4} = 3, \quad r_2 = \sqrt{1^2 + 2^2 + 11} = 4 \] The line joining centers: \[ \text{Find radical axis of circles} \Rightarrow \text{line} \ 4x + 8y - 7 = 0 \]
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