Question

Write an equation of a circle with the given center and radius.center (4, 5), radius 7

Answer 1

Quadratic relations and comic sections unit test part 1

6. b. (x-4)^2 + (y-5)^2 = 49

Answer 2

To solve this, we are going to use the center-radius form of a circle equation:
`(x-h)^(2)+(y-k)^(2)=r^(2)`
where

`(h,k)` is the center of the circle

`r` is the radius of the circle

Since the center of our circle is
`(4,5)`,
`h=4` and
`k=5`. We also now that its radius is 7, so
`r=7`. Lets replace those values in our equation:

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

`(x-4)^(2)+(y-5)^(2)=7^(2)`

We can conclude that the equation of a circle with center at the point (4,5) and radius 7, is
`(x-4)^(2)+(y-5)^(2)=7^(2)`