# Determine the equation of a circle

• Oct 17th 2009, 06:26 AM
mamt6
Determine the equation of a circle
Determine the standard equation for the circle
C that passes through
the points
A
(2, 0) and B(0, 4), and has centre lying on the line L : x+2y+4 = 0.

Hint: First find the centre of C ; it has the same distance from A and B.

Thanks for at least looking at the question
• Oct 17th 2009, 07:22 AM
skeeter
Quote:

Originally Posted by mamt6
Determine the standard equation for the circle
C that passes through
the points
A
(2, 0) and B(0, 4), and has centre lying on the line L : x+2y+4 = 0.

Hint: First find the centre of C ; it has the same distance from A and B.

Thanks for at least looking at the question

let point C be (x,y) ...

\$\displaystyle AC = BC\$

\$\displaystyle (x-2)^2 + (y-0)^2 = (x-0)^2 + (y-4)^2\$

\$\displaystyle x^2 - 4x + 4 + y^2 = x^2 + y^2 - 8y + 16\$

\$\displaystyle -4x + 4 = -8y + 16\$

\$\displaystyle -x + 1 = -2y + 4\$

\$\displaystyle x = 2y-3\$

since (x,y) lies on the line \$\displaystyle x+2y+4=0\$ ... \$\displaystyle x = -2y-4\$

so ...

\$\displaystyle -2y-4 = 2y-3\$

solve for the y-coordinate of point C , then find its x-coordinate.

then determine the equation of the circle ...

\$\displaystyle (x - x_c)^2 + (y - y_c)^2 = r^2\$