1 Answer

Jamesconant · Answer 1 · 2023-09-05T19:06:23+0000

Write an equation in general form of the circle with the given properties.

Ends of diameter at (5,7) and (-5,-7)

we have that

the equation of the circle is

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

where (h,k) is the center and r is the radius

step 1

Find the center

Remember that

The center of the circle is the midpoint of diameter

so

$\begin{gathered} (h,k)=((5-5)/(2),(7-7)/(2)) \\ (h,k)=(0,0) \end{gathered}$

the center is the origin

step 2

Find the radius

Find the diameter

calculate the distance between two points

$\begin{gathered} d=\sqrt[\square]{(-7-7)^2+(-5-5)^2} \\ d=\sqrt[\square]{(-14)^2+(-10)^2} \\ d=\sqrt[\square]{296} \end{gathered}$

simplify

$D=\sqrt[\square]{296}=2\sqrt[\square]{74}$

the radius is half the diameter

so

r=2√74/2=√74

step 3

the equation iof the circle is

x^2+y^2=(√74)^2

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