Answer:
The equation of the circle is (x + 10)² + (y + 5)² = 125 in standard form
Step-by-step explanation:
* lets study the standard form of the equation of a circle
- If the coordinates of the center of the circle are(h , k) and its radius
is r, then the standard equation of the circle is:
(x - h)² + (y - k)² = r²
* Now lets solve the problem
∵ The coordinates of the center of the circle are (-10 , -5)
∵ The standard form of the equation is (x - h)² + (y - k)² = r²
∵ h , k are the coordinates of the center
∴ h = -10 , k = -5
∴ The equation of the circle = (x - -10)² + (y - -5)² = r²
∴ The equation of the circle = (x + 10)² + (y + 5)² = r²
- To find the value of the radius lets use the point (-5 , 5) to
substitute their coordinate instead of x and y in the equation
∵ The circle passes through point (-5 , 5)
∵ (x + 10)² + (y + 5)² = r²
- Use x = -5 and y = 5
∴ (-5 + 10)² + (5 + 5)² = r² ⇒ simplify
∴ (5)² + (10)² = r²
∴ 25 + 100 = r²
∴ r² = 125
* Now lets write the equation in standard form
∴ (x + 10)² + (y + 5)² = 125
* The equation of the circle is (x + 10)² + (y + 5)² = 125 in standard form
