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

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

Explanation:

step 1

Find the radius of the circle

we know that

The distance between the center and any point that lie on the circle is equal to the radius

we have the points

(5,-4) and (-3,2)

the formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

substitute the values

`r=\sqrt{(2+4)^(2)+(-3-5)^(2)}`

`r=\sqrt{(6)^(2)+(-8)^(2)}`

`r=√(100)\ units`

`r=10\ units`

step 2

Find the equation of the circle

we know that

The equation of a circle in standard form is equal to

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

where

(h,k) is the center

r is the radius

we have

`(h,k)=(5,-4)\\r=10\ units`

substitute

`(x-5)^2+(y+4)^2=10^2`

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