165k views
5 votes
What is the equation of the circle whose diameter has endpoints (9,1) and (9,15)

1 Answer

6 votes

\text{The equation }of\text{ circle: }(x-9)^2+(y-8)^2=49

Step-by-step explanation:

Given endpoints (9,1) and (9,15)

The equation of circle:


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

To find (a, b) which is the center of the circle, we will apply the midpoint formula:


\text{Midpoint = }(1)/(2)(x_1+x_2),\text{ }(1)/(2)(y_1+y_2)


\begin{gathered} \text{Midpoint =1/2}(9+9),\text{ 1/2(1+15) } \\ Midpoint=\text{ 9, 8} \\ \text{Center = }(a,\text{ b) = 9, 8} \end{gathered}

To find the radius (r), we need to find the distance between the center an any of the two points.

Using (9, 8) and (9, 1)


dis\tan ce\text{ formula= }\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}
\begin{gathered} \text{distance = }\sqrt[]{(1-8)^2+(9-9)^2} \\ =\text{ }\sqrt[]{(-7)^2+(0)^2}\text{ = }\sqrt[]{49+0} \\ \text{Distance = }\sqrt[]{49\text{ }}=\text{ 7} \\ \text{radius = 7} \end{gathered}
\begin{gathered} Inserting\text{ the values in }(x-a)^2+(y-b)^2=r^2\text{ } \\ \text{The equation }of\text{circle: }(x-9)^2+(y-8)^2=7^2 \\ \text{The equation }of\text{ circle: }(x-9)^2+(y-8)^2=49 \end{gathered}

User VBMali
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories