Question

Find the centre of the circle, if the equation of the circle is given x2+y2+2x-6y-15=0. The center is

Answer 1

[AI-generated answer — Bot GPT 3.5]

The equation of a circle is generally in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) are the coordinates of the center and r is the radius.

To put the given equation in this form, we complete the square for the x and y terms:

x^2 + 2x + y^2 - 6y - 15 = 0

(x^2 + 2x + 1) + (y^2 - 6y + 9) = 15 + 1 + 9

(x + 1)^2 + (y - 3)^2 = 25

Comparing this to the general form, we can see that the center is at (-1, 3).