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Slope Form of Tangent

Find locus of...

Question

Find locus of $3 r d$ vertex of right angled triangle $.$ The ends of whose hypotenuse are $(4, 0)$ $(0, 4) ?$

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Solution

Let $P (x, y)$ be the point $.$
slope of $1 s t$ side $= (y - 4) / x .$
slope of $2 n d$ side $y / (x - 4) .$
By this property $,$
$y (y - 4) / x (x - 4) = - 1.$
$y^{2} - 4 y = 4 x - x^{2}$
$x^{2} + y^{2} - 4 x - 4 y = 0$ is a locus of required points $.$

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