Question

What is the equation of the circle shown?

Answer 1

Answer:

(x + 4)² + (y - 2)² = 8

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 ) = (- 4, 2 ) , then

(x - (- 4))² + (y - 2)² = r²

(x + 4)² + (y - 2)² = r²

CA is the radius of the circle

To find r use the distance formula

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

with (x₁, y₁ ) = C(- 4, 2) and (x₂, y₂ ) = A(- 2, 4)

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

  = $\sqrt{2^2+2^2}$

  = $\sqrt{8}$ , then r² = ($\sqrt{8}$ )² = 8

Then

(x + 4)² + (y - 2)² = 8 ← equation of circle