Question

Find the equation to the locus of the point for which the square of whose distance from origin is 4 times it's y-coordinate

Answer 1

let x,y be locus point

distance from origin to the locus point is

$distance \: from \: origin \: \: to \: locus \: point \: = \sqrt{ {x}^{2} + {y}^{2} } \\ from \: the \: question \: given \: that \\ square \: of \: distance \: from \: origin \: is \: equal \: to \: four \: times \:t he \: y - ordinate \\ so \: \: {x}^{2} + {y}^{2} = 4y$

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