JEE Main2004MathematicsParabolaActual

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=4 q y
B(x-q)^2=4 p y
C(y-p)^2=4 q x
D(y-q)^2=4 p x

Correct answer

A. (x-p)^2=4 q y

Step-by-step 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 aligned & x^2-(h+p) x+(h p+k q)=0 (h+p)^2=4(h p+k q) (D=0) & (x-p)^2=4 q y . aligned

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