Question

The radius of largest and smallest circle passing through point root 3 root 2 and touching circle x square + y square + 2 root 2 y - 2 = 20 are r1 and r2 respectively find the difference between r1 and r2

Answer 1

The difference of largest circle and smallest circle =$2\sqrt{6}$

Step-by-step explanation:

Since, both the circles pass through point A$(\sqrt3, \sqrt2)$.

• The equation of touching circle is given as;

                             $x^2 + y^2 + 2\sqrt2 y - 2 = 20$

•  $x^2 + y^2 + 2\sqrt2 y +2 - 2 = 20 + 2$

•  $x^2 + (y + \sqrt2 )^2 - 2 = 22$

•  $x^2 + (y + \sqrt2 )^2 = (2\sqrt6)^2$

Thus, we have the coordinate of the center of touching circle as C $(0,-\sqrt{2})$ and radius (r) is $2\sqrt{6}$.

we know that,

• The radius of smallest circle$r_1 = \dfrac{AC-r}{2}$

• The radius of largest circle$r_2 = \dfrac{AC+r}{2}$

•  Difference of radii =$r_2 - r_1$

                              =$\dfrac{AC+r}{2} - \dfrac{AC-r}{2}$

                              = r

                              $= 2\sqrt{6}$