Question

The center of a circle and a point on the circle are given. Write the equation of the circle in standard form.

center: (2,-5), point on the circle: (-4,-5)

Answer 1

25= (x-2)² + (y+4)²

Hope this helps!!!

Answer 2

`(x-2)^2+(y+5)^2=36`

Explanation:

The standard form of a circle is given by the equation:

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

Where (h, k) is the center and r is the radius.

We know that the center is (2, -5). So, we can substitute 2 for h and -5 for k. This yields:

`(x-(2))^2+(y-(-5))^2=r^2`

Simplify:

`(x-2)^2+(y+5)^2=r^2`

Now, we need to determine r. We know that a point on the circle is (-4, -5). Thus, we can determine r by substituting -4 for x and -5 for y. This yields:

`(-4-2)^2+(-5+5)^2=r^2`

Evaluate:

`(-6)^2+(0)^2=r^2`

Evaluate:

`36=r^2`

Hence, the radius squared is 36.

We do not actually need to solve for r, as we will square it anyways.

We will substitute 36 for r squared. Hence, our equation is:

`(x-2)^2+(y+5)^2=36`

The radius will thus be 6 units.