Question

Find an equation of the circle that has center (-1,6) and passes through (-6,1)

Answer 1

Answer:

(x + 1)² + (y - 6)² = 50

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.

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 ) = (- 1, 6) and (x₂, y₂ ) = (- 6, 1)

r = $\sqrt{(-6+1)^2+(1-6)^2}$

  = $\sqrt{(-5)^2+(-5)^2}$

  = $\sqrt{25+25}$

  = $\sqrt{50}$

(h, k ) = (- 1, 6 ), then

(x - (- 1))² + (y - 6)² = ($\sqrt{50}$ )² , that is

(x + 1)² + (y - 6)² = 50 ← equation of circle