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Equation of the Circle Using End Points of Diameter

Find the equa...

Question

Find the equation of the circle with
Centre (-a, -b) and radius $\sqrt{a^{2} - b^{2}}$

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Solution

Here $h = - a, k = - b a n d r = \sqrt{a^{2} - b^{2}}$
The equation of circle is,
$(x - h)^{2} + (y - k)^{2} = r^{2} ∴ (x + a)^{2} + (y + b)^{2} = (\sqrt{a^{2} - b^{2}})^{2} \Rightarrow x^{2} + a^{2} + 2 a x + y^{2} + b^{2} + 2 b y = a^{2} - b^{2} \Rightarrow x^{2} + y^{2} + 2 a x + 2 b y + 2 b^{2} = 0$

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