Question

Find the equation for the circle with center ​(4​,3​) and passing through ​(2​,-4​)

Answer 1

Answer:

$(x - 4)^{2} + (y - 3)^{2} = 53$

Step-by-step explanation:

The general equation of a circle is as follows:

$(x - x_{c})^{2} + (y - y_{c})^{2} = r^{2}$

In which the center is $(x_{c}, y_{c})$, and r is the radius.

In this problem, we have that:

$x_{c} = 4, y_{c} = 3$

So

$(x - 4)^{2} + (y - 3)^{2} = r^{2}$

Passing through ​(2​,-4​)

We replace into the equation to find the radius.

$(2 - 4)^{2} + (-4 - 3)^{2} = r^{2}$

$4 + 49 = r^{2}$

$r^{2} = 53$

The equation of the circle is:

$(x - 4)^{2} + (y - 3)^{2} = 53$