The lines y=(2/3)x+2 and y=(-2/3)x+12 are tangent to circle C at the points (3,4) and (3,10), respectively.

Question

a) Find the coordinates of C and the radius of circle C. Explain your reasoning.

b)Write the standard equation of circle C.

Answer 1

Two radii of the circle are the lines perpendicular to the given lines. They are
y = -3/2 (x-3)+4
y = 3/2 (x-3)+10
They intersect at the center of the circle: (1,7)
The radius of the circle is r^2 = (1-3)^2 + (7-4)^2 = 13
The circle is (x-1)^2 + (y-7)^2 = 13

Answer 2

Thanks for your response oobleck!

When finding radii equations, why did you say "(x-3)?"

Answer 3

review the point-slope form of a line.
the line with slope m through (h,k) is
y-k = m(x-h)