Question

Find the center and radius of the given circle and graph it.

15. x^2+y^2+10y+21=0

Answer 1

Find the center and radius of the given circle and graph it.

$$x ^ {2} + y ^ {2} + 10y + 21 = 0$$

**Solution:**

Reduce the following equation to its canonical form

$$x ^ {2} + y ^ {2} + 10y + 21 = 0$$ $$x ^ {2} + (y ^ {2} + 10y + 25) - 4 = 0$$ $$x ^ {2} + (y + 5) ^ {2} = 4$$ $$x ^ {2} + (y + 5) ^ {2} = 2 ^ {2}$$

Then

$$C (0, - 5) \quad R = 2$$

Answer: $C(0, - 5)$ $R = 2$