Question

Find the radius of circle concentric with $x^2+y^2-8x+6y+10=0$ and passing through origin.

• A. $5$
• B. $10$
• C. $5\sqrt{2}$
• D. $10\sqrt{2}$

Answer 1

The correct option is A $5$

Center of the given circle $C=(4,-3)$

We now have to find a circle which has center C and passes through origin

Let $(x–4{)}^2+(y+3{)}^2=r^2$ be the equation of the circle

Since it passes through $(0,0)$

$-4^2+3^2=r^2$

$⟹r^2=25⟹r=5$

Equation is $(x–4{)}^2+(y+3{)}^2=25$

$x^2+y^2-8x+6y=0$