Question:
A variable circle passes through the fixed point A (p, q) and touches x-axis. The locus of the other end of the diameter through A is
A variable circle passes through the fixed point A (p, q) and touches x-axis. The locus of the other end of the diameter through A is
Updated On: Jul 27, 2022
- $(x - p)^2 = 4qy$
- $(x - q)^2 = 4py$
- $(y - p)^2 = 4qx$
- $(y - q)^2 = 4px$
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The Correct Option is A
Solution and Explanation
Let the other end of diameter is (h, k) then equation of circle is
$(x - h)(x - p) + (y - k)(y - q) = 0$
Put $y = 0$, since x-axis touches the circle
$? x^2 - (h + p)x + (hp + kq) = 0 ? (h + p)^2 = 4(hp + kq) \quad (D = 0)$
$? (x - p)^2 = 4qy$.
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