Question

Determine the equation of the circle graphed below. ( please help me )

Answer 1

Answer:

(x - 3)² + (y + 5)² = 10

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k) = (3, - 5 ) , then

(x - 3)² + (y - (- 5) )² = r² , that is

(x - 3)² + (y + 5)² = r²

r is the distance from the centre to a point on the line

Calculate r using the distance formula

r = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }$

with (x₁, y₁ ) = (3, - 5) and (x₂, y₂ ) = (6, - 4)

r = $\sqrt{(6-3)^2+(-4+5)^2}$

  = $\sqrt{3^2+1^2}$

  = $\sqrt{9+1}$

   = $\sqrt{10}$ ⇒ r² = ($\sqrt{10}$ )² = 10

(x - 3)² + (y + 5)² = 10 ← equation of circle