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

sjeikdom0

sjeikdom0

Answered question

2020-11-08

Write the equation of each circle
Radius of 8 , center at the intersection of x+2y=8 and 2x3y=5

Answer & Explanation

Ayesha Gomez

Ayesha Gomez

Skilled2020-11-09Added 104 answers

First, we find the center of the circle by solving the system of equations: x+2y=8
2x3y=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:
(xh)2+(yk)2=r2
(x2)2+(y3)2=82
(x2)2+(y3)2=64

Jeffrey Jordon

Jeffrey Jordon

Expert2021-08-10Added 2605 answers

Answer is given below (on video)

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