Find the equation of the circle with center at (-3, 1) and through the point (2, 13).

What is the center and radius of the following circle: x^2 + (y – 6)^2 = 50

What is the diameter of the following circle: (x + 4)^2 + (y – 9)^2 = 18

What is the equation of the circle with center at (-3, 0) and diameter 20?

What is the center and radius of the following circle: (x – 5)^2 + (y + 2)^2 = 16

Question1. We want to find the equation of the circle with center at (-3, 1) and through the point (2, 13).

Use the distance formula to find the radius.

The equation of the circle is given by:

Where (a,b)=(-3,1) is the center and r=13 is the radius.

We substitute to get:

Question 2) The given circle has equation:

We want to find the center and radius of this circle.

We need to compare to

Rewriting the given equation will make it easy for us;

Therefore the center is (0,6) and the radius is

Question 3. We want to find the diameter of the circle with equation:

By comparing to

We have

By the diameter is twice the radius.

Question 4. We want to find the equation of the circle with center at (-3, 0) and diameter 20.

We use the formula:

where (a,b)=(-3,0) is the center and r=20 is the radius.

Question 5) We want to find the center and radius of

We compare this equation to

Then we can see that:

Therefore the center is ((5,-2) and the radius is 4.

20

step-by-step explanation: