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Analytical Geometry

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2 Jul 2009 19:54:48 IST

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a variable line passes through point (h,k) find the locus of foot of perpendicular drawn to line fro

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a variable line passes through point (h,k) find the locus of foot of perpendicular drawn to line from origin

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Krishna Gopal Singh

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Joined: 29 Dec 2006

Posts: 4965

4 Jul 2009 00:24:52 IST

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If slope of line is m then equation of line is (y-k) = m(x-h)

For foot of perpendicular y/x = -1/m

Solving the two we get

y(1+m^2) = (k-mh)

Putting m = -x/y we get

y*(1+ x^2/y^2) = (k+ hx/y)

Or x^2 + y^2 = (ky + hx)

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