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

Substituting the respective values :-

`\implies ( x - 4 )^2 + \{y - (-2)\}^2 = (√(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 }}`