Question

Type the correct answer in each box. A circle is centered at the point (5, -4) and passes through the point (-3, 2). The equation of this circle is (x + )2 + (y + )2 = .

Answer 1

-5

4

100

Explanation:

Answer 2

`(x+ \boxed{-5})^2+(y+\boxed4)^2=\boxed{100}`

Explanation:

Given:

Center of circle is at (5, -4).

A point on the circle is
`(x_1,y_1)=(-3, 2)`

Equation of a circle with center
`(h,k)` and radius 'r' is given as:

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

Here,
`(h,k)=(5,-4)`

Radius of a circle is equal to the distance of point on the circle from the center of the circle and is given using the distance formula for square of the distance as:

`r^2=(h-x_1)^2+(k-y_1)^2`

Using distance formula for the points (5, -4) and (-3, 2), we get

`r^2=(5-(-3))^2+(-4-2)^2\\r^2=(5+3)^2+(-6)^2\\r^2=8^2+6^2\\r^2=64+36=100`

Therefore, the equation of the circle is:

`(x-5)^2+(y-(-4))^2=100\\(x-5)^2+(y+4)^2=100`

Now, rewriting it in the form asked in the question, we get

`(x+ \boxed{-5})^2+(y+\boxed4)^2=\boxed{100}`