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:

Equation of a circle

`(x-a)^2+(y-b)^2=r^2`

where:

• (a, b) is the center
• r is the radius

Given:

• center = (5, -4)
• point on circle = (-3, 2)

Substitute the given values into the circle equation and solve for r:

`\implies r^2=(-3-5)^2+(2-(-4))^2`

`\implies r^2=(-8)^2+(6)^2`

`\implies r^2=64+36`

`\implies r^2=100`

`\implies r=√(100)`

`\implies r=10`

Substitute the given center and the found value of r into the circle equation to create the equation of the circle:

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

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