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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
(xp)2=4qy
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B
(xq)2=4py
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C
(yp)2=4qx
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D
(yq)2=4px
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Solution

The correct option is A $$(x-p)^2=4qy$$
$$\Rightarrow (h-p)^2+(k-q)=4\left(\dfrac{k+q}{2}\right)^2$$
$$=k^2+2kq+q^2$$
$$\Rightarrow (x-p)^2=4qy$$.
1323600_1641722_ans_d0a8125cd4054522a7e70e42f3b19dd6.PNG

Mathematics

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