125k views
4 votes
Find the equation of the circle having the given properties:

Find the equation of the circle having the given properties:-example-1

1 Answer

5 votes

The equation of a circle is given by:


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

3.

Using the points (4, 0), (0, 2) and (0, 0), we have:


\begin{gathered} (0,0)\colon \\ h^2+k^2=r^2 \\ (0,2)\colon \\ h^2+(2-k)^2=r^2 \\ h^2+4-2k+k^2=r^2 \\ \text{Comparing both equations:} \\ h^2+k^2=h^2+4-2k+k^2 \\ 4-2k=0 \\ k=2 \\ (4,0)\colon \\ (4-h)^2+k^2=r^2 \\ 16-8h+h^2+4=r^2 \\ \text{Comparing this last equation with the first one:} \\ 16-8h+h^2+4=h^2+4 \\ 16-8h=0 \\ h=2 \\ \\ h^2+k^2=r^2 \\ r^2=4+4=8 \end{gathered}

So the equation of this circle is:


(x-2)^2+(y-2)^2=8

User Nickesha
by
7.9k 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