Determine the equation of the circle with center (0,−1) containing the point (−√35,0)

Answer 1

The standard equation for a circle with center (h,k) and radius r is:

(x - h)^2 + (y - k)^2 = r^2

In this case, we know that the center is (0,-1). Therefore, we have:

(x - 0)^2 + (y + 1)^2 = r^2

We also know that the circle contains the point (-√35,0). We can substitute these values into our equation to solve for the radius, r:

(-√35 - 0)^2 + (0 + 1)^2 = r^2
35 + 1 = r^2
r = √36
r = 6

So our equation becomes:

x^2 + (y + 1)^2 = 36

Therefore, the equation of the circle with center (0,-1) and containing the point (-√35,0) is x^2 + (y + 1)^2 = 36.