Question

A circle is centered at the point (-3, 2) and passes through the point (1, 5). The radius of the circle is___ units. The point (-7,__ ) lies on this circle.
Fill in the blanks

Answer 1

A circle is centered at the point (-3, 2) and passes through the point (1, 5). The radius of the circle is 5_ units. The points(-7,5) and (-7,-1) lie on this circle.

Answer 2

The radius of the circle is $\boxed{5{\text{ units}}}$ and the point that lies on the circle is $\boxed{\left( { - 7,5} \right)}$ and $\boxed{\left( { - 7,-1} \right)}.$

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 $\left( {1,5} \right).$

The point that lies on the circle is  

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.

Substitute $-7$ for  $x$, $5$ for $r$, $-3$ for h and 2 for k in general equation of the circle to obtain the y-coordinate of point.

$\begin{aligned}{\left( {y - 2} \right)^2} &= 9\\y - 2&= \sqrt 9\\ y - 2 &= \pm 3 \\ y - 2&= 3\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,or\,\,\,\,\,\,\,\,\,\,y - 2= - 3\\y &=5\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,or\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,y = - 1\\\end{aligned}$

The radius of the circle is $\boxed{5{\text{ units}}}$ and the point that lies on the circle is $\boxed{\left( { - 7,5} \right)}$ and $\boxed{\left( { - 7,-1} \right)}.$

Learn more:

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

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

3. Learn more about coplanar 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.