Question

23) Find the center of the circle

Answer 1

Given Equation of Circle :-

$\bull\:$$\sf{x^2+y^2 -10x+8y + 1= 0}$

Solution:-

The general form of circle is given by the equation by the equation -

$\green{ \underline { \boxed{ \sf{x^2+y^2 + 2gx+2fy + c = 0}}}}$

in which

• coordinate of center = (-g , -f )
• radius of circle = $\sqrt{g^2+f^2-c}$

❀ Comparing given equation with general form of circle -

• g = -5
• f = 4
• c = 1

So, Center of Circle = (-(-5), -4)

➥ (5, -4)

Also, radius of circle = $\sqrt{(-5)^2+4^2-1}$

➥ $\sqrt{25+16-1}$

➥ $\sqrt{40}$

➥ $2\sqrt{10}$ units .