Question

Determine the equation of the circle graphed below.

Answer 1

We need to determine the equation of the circle graphed in the attachment. Firstly we know the Standard equation of a Circle as ,

$\sf\implies (x-h)^2+(y-k)^2 = r^2$

• Where ( h , k ) is centre and r is radius.

Let's find out the radius . As ,

$\sf\implies r = \sqrt{ ( 6-4)^2+(2+2)^2} \\\\ \sf\implies r =\sqrt{ 2^2 + 4^2}\\\\\sf\implies r = \sqrt{ 4 + 16 }\\\\\sf\implies \red{r =\sqrt{20}}$

Substituting the respective values :-

$\implies ( x - 4 )^2 + \{y - (-2)\}^2 = (\sqrt{20})^2 \\\\\sf\implies ( x - 4 )^2 + \{y + 2 \}^2 = 20 \\\\\sf\implies x^2+16-8x + y^2+4+4y = 20 \\\\\sf\implies \red{x^2+ y^2 - 8x + 4y = 0 }$

Answer :-

$\boxed{\pink{\tt Equation \to x^2+ y^2 - 8x + 4y = 0 }}$