CircleEasy
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
Options
A.(x - p)2 = 4qy
B.(x - q)2 = 4py
C.(y - p)2 = 4qx
D.(y - q)2 = 4px
Solution
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
⇒ x2 - (h + p)x + (hp + kq) = 0 ⇒ (h + p)2 = 4(hp + kq) (D = 0)
⇒ (x - p)2 = 4qy.
(x - h)(x - p) + (y - k)(y - q) = 0
Put y = 0, since x-axis touches the circle
⇒ x2 - (h + p)x + (hp + kq) = 0 ⇒ (h + p)2 = 4(hp + kq) (D = 0)
⇒ (x - p)2 = 4qy.
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