Question

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

Systems of equations

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

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:
$$\displaystyle{\left({x}-{h}\right)}^{{2}}+{\left({y}-{k}\right)}^{{2}}={r}^{{2}}$$
$$\displaystyle{\left({x}-{2}\right)}^{{2}}+{\left({y}-{3}\right)}^{{2}}={8}^{{2}}$$
$$\displaystyle{\left({x}-{2}\right)}^{{2}}+{\left({y}-{3}\right)}^{{2}}={64}$$

2021-08-10

Answer is given below (on video)