The line x-2y+22=0 is tangent to a circle at (0,11). The line y=2x+2 is tangent to the same circle at (3,8). Find the center of the circle.

Question

The line x-2y+22=0 is tangent to a circle at (0,11). The line y=2x+2 is tangent to the same circle at (3,8). Find the center of the circle.

Answer 1

Determine slope of x - 2y = 22, label m₁

Take negative reciprocal of slope, -1 / m₁ this is slope a one radius

Determine equation of line with slope -1 / m₁ and passing through (0,11). This is line₁.

Determone slope of y = 2x + 2. label m₂.

Take negatrive reciprocal of slope, -1 / m₂ this is slope of other radius.

Determine equation of line with slope -1 / m₂ and passing through (3,8). This is line₂.

The intersection of line₁ and line₂ is the center of the circle.