Question

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

Answer 1

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 $(x-4)^{2}+(y-5)^{2}=7^{2}$

Answer 2

Quadratic relations and comic sections unit test part 1

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