Through a fixed point (h,k), secant are drawn to the circle $x^{2} + y^{2} = r^{2}$ . Show that the locus of the midpoints of the secants by the circle is $x^{2} + y^{2} = h x + k y$ .

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Through a fixed point (h,k), secant are drawn to the circle

x^{2} + y^{2} = r^{2}

. Show that the locus of the midpoints of the secants by the circle is

x^{2} + y^{2} = h x + k y

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Question Text

Through a fixed point (h,k), secant are drawn to the circle

x^{2} + y^{2} = r^{2}

. Show that the locus of the midpoints of the secants by the circle is

x^{2} + y^{2} = h x + k y

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