Question

Find the equation of a circle if:
(i)center (a,b) and radius $\sqrt{a^2+b^2}$
(ii)center $(a\sec \alpha ,b\tan \alpha )$ and radius $\sqrt{a^2{\sec }^2\alpha +b^2{\sec }^2\alpha }$

Answer 1

Equation of circle will be

(i) $(x-a{)}^2+(y-b{)}^2=(\sqrt{a^2+b^2}{)}^2$

$x^2-2ax+y^2-2by=0$

(ii) $(x-asec\alpha {)}^2+(y-btan\alpha {)}^2=(\sqrt{a^{2}se{c}^2\alpha +b^{2}ta{n}^2\alpha }{)}^2$

$x^2-2axsec\alpha +y^2-2bytan\alpha =0$