Identify the equation of the circle x that passes through (−3,−5) and has center (4,−7).

(x - 4)² + (y + 7)² = 53

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, - 7), so

(x - 4)² + (y + 7)² = r²

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

Use the distance formula to calculate r

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (4, - 7) and (x₂, y₂ ) = (- 3, - 5)

r =

  = = =

Hence r² = ( )² = 53

(x - 4)² + (y + 7)² = 53 ← equation of circle

if you use photomath right away it will give you the answer not like this app that you have to wait for people.