Question bank/JEE Main/Mathematics

A variable circle passes through fixed point A(p, q) and touches
x-axis. The locus of the other end of the diameter through A is,d pj o`Ùk fLFkj fcUnq A(p,q) ls xqtjrk gS rFkk x- s A ls xqtjus okys O;kl

A$(x - p)^{2} = 4qy$B$(x - q)^{2} = 4py$C$(y - p)^{2} = 4qx$D$(y - q)^{2} = 4px$

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$CM = \frac{AB}{2} \Rightarrow \left| \frac{q + y}{2} \right| = \frac{\sqrt{(x - p)^{2} + (y - q)^{2}}}{2} \Rightarrow (x - p)^{2} = 4qy$

Source: Grass-G / M-25 Mathematics Paper 7 Jan.docx