Question

The circle below is centered at the point (-1,2) and has a radius of length 3. What is it’s equation

Answer 1

Answer:(x + 1)^2 + (y - 2)^2 = 9

Explanation:

The equation of a circle with center coordinates (h, k) and radius r is given by:

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

In this case, the center of the circle is (-1, 2) and the radius is 3. Plugging these values into the equation, we have:

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

Simplifying:

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

So, the equation of the circle is (x + 1)^2 + (y - 2)^2 = 9.

Answer 2

The format of a circle's equation is:

`\mapsto\phantom{333}\bf{(x-h)^2+(y-k)^2=r^2}`

where:

• (h,k) is the center of the circle
• r is the radius

Stick in the data:

`\mapsto\phantom{333}\bf{(x-(-1)^2+(y-2)^2=3^2}`

Simplify:

`\mapsto\phantom{333}\bf{(x+1)^2+(y-2)^2=9}`

Hence, this is the equation.