Question

Write the equation of each circleRadius of 8 , center at the intersection of x + 2y = 8 and 2x - 3y = -5

Systems of equations
ANSWERED
asked 2020-11-08

Write the equation of each circle
Radius of 8 , center at the intersection of \(x + 2y = 8\) and \(2x - 3y = -5\)

Expert Answers (2)

2020-11-09

First, we find the center of the circle by solving the system of equations: \(x+2y=8\)
\(2x-3y=-5\)
Multiply (1) by (2) to obtain (3):
\(2x+4y=16\)
Subtract each side of (2) adn (3) to eliminate 2x and solve for y:
\(-7y=-21\)
\(y=3\)
Solve for x using (1):
\(x+2(3)=8\)
\(x+6=8\)
\(x=2\)
The point of intersection is the center:\((h,k)=(2,3)\)
The equation of the circle with center (h,k) and radius r is given by:
\(\displaystyle{\left({x}-{h}\right)}^{{2}}+{\left({y}-{k}\right)}^{{2}}={r}^{{2}}\)
\(\displaystyle{\left({x}-{2}\right)}^{{2}}+{\left({y}-{3}\right)}^{{2}}={8}^{{2}}\)
\(\displaystyle{\left({x}-{2}\right)}^{{2}}+{\left({y}-{3}\right)}^{{2}}={64}\)

4
 
Best answer
2021-08-10

Answer is given below (on video)

10

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