Write Equation of Circle from Key Features

Question

Determine the equation of the circle with center (0,-5) containing the points (-√109,-6)

Answer 1

Equations of a circle are in the form (x-h)^2 + (y-k)^2 = r^2 where (h, k) is the center and r is the radius. So we have our center but we don't have our radius r, but we do have the point (-√109, -6), so we can plug that point in for x and y and plug in our center for h and k to find r^2. Now you have your center and r^2, and you can put those into the final form. Hope that helps!

Answer 2

circle's center = (0,-5) and the circle contains the point (-sqr109, -6)

(sqr109)^2 + (-6+5)^2 = r^2

109 +1 = r^2

r^2 =110

the circle's equation is x^2 + (y+5)^2 = 110

or if you want expand and combine the constants

x^2 +y^2 + 10y = 85

Answer 3

that r²=110 is a little tricky

and that center is at y= -5

means equation is x²+(y+5)²=110

check,,,,when y= -6, x=+/-√109