Question

write the equation in standard form for the circle with center (0,5) and radius 1

Answer 1

Hey, look, all you really need is the first line

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

Answer 2

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

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

Substituting the given values, we get:

(x-0)^2 + (y-5)^2 = 1^2

Simplifying and expanding, we get:

x^2 + y^2 - 10y + 25 = 1

x^2 + y^2 - 10y + 24 = 0

Therefore, the equation in standard form for the circle with center (0,5) and radius 1 is:

x^2 + y^2 - 10y + 24 = 0.

Answer 3

That's correct! The general equation of a circle with center (h,k) and radius r is:

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

This form of the equation is called the standard form of the equation of a circle.