Question

determine the equation of the circle if its center is (8,-6) and which passes through the points (5,-2).

Answer 1

Answer:

(x - 8)² + (y + 6)² = 25

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 ) = (8, - 6 ) , then

(x - 8)² + (y - (- 6))² = r² , that is

(x - 8)² + (y + 6)² = r²

The radius is the distance from the centre to a point on the circle

Calculate r using the distance formula

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

with (x₁, y₁ ) = (8, - 6 ) and (x₂, y₂ ) = (5, - 2 )

r = $\sqrt{(5-8)^2+(-2-(-6))^2}$

  = $\sqrt{(-3)^2+(-2+6)^2}$

  = $\sqrt{9+4^2}$

  = $\sqrt{9+16}$

   = $\sqrt{25}$

   = 5

Then equation of circle is

(x - 8)² + (y + 6)² = 5² , that is

(x - 8)² + (y + 6)² = 25