Question

A circle is centered at the point (-3,2) and passes through the point (1,5). What's the radius

Answer 1

radius = square root (( x2-x1)^2 +(y2-y1)^2)

 = sqrt(1-(-3)^2+(5-2)^2

= sqrt(16+9)

=sqrt(25)

= 5

radius is 5

Answer 2

The radius of the circle is $\boxed{5{\text{ units}}}.$

Further explanation:

The standard equationof the circle with center $\left( {h,k}\right)$ and radius r can be expressed as,

${\left( {x - h}\right)^2} + {\left({y - k} \right)^2}= {r^2}.$

Given:

A circle with center at $\left({ - 3,2} \right).$

The passing through point is $\left( {1,5} \right).$

Explanation:

The center is at $\left( { - 3,2} \right).$

The passing through point is $\left( {1,5} \right)$. Therefore, the point satisfies the equation of circle.

Substitute 1 for x, 5 for y, -3 for h and 2 for k in general equation of the circle to obtain the radius of circle.

$\begin{aligned}{\left( {x - h}\right)^2}+{\left({y - k}\right)^2}&={r^2}\\{\left( {1 + 3} \right)^2} + {\left( {5 - 2}\right)^2}&= {r^2}\\16 + 9&= {r^2}\\\sqrt{25}&= r\\5&= r\\\end{aligned}$

The radius of the circle is $\boxed{5{\text{ units}}}.$

The radius of the circle is $\boxed{5{\text{ units}}}.$

Learn more:

1. Learn more about equation of circle brainly.com/question/1506955.

2. Learn more about domain of the function https://brainly.com/question/3852778.

3. Learn more about coplanar https://brainly.com/question/4165000.

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Circle

Keywords: Circle, centered point, (-3,2), passes point (1,5), standard form of the circle, equation of the circle, center, diameter of circle, radius of the circle,center-radius form, general equation of circle, tangent, area of circle.