Thread: analytic geometry (circles)

Find the equation of the circle of radius tangent to the line 2x+y-3=0 and having its center on the line 2x+3y = 4.

Originally Posted by TechnicianEngineer

Find the equation of the circle of radius tangent to the line 2x+y-3=0 and having its center on the line 2x+3y = 4.

To do this we must find a point having distance of from .

how am i supposed to solve the line perpendicular to the tangent line when i have two unknowns (the coordinates at the center and the end of the circle)

Originally Posted by TechnicianEngineer

how am i supposed to solve the line perpendicular to the tangent line when i have two unknowns (the coordinates at the center and the end of the circle)

You are not supposed to do that.

You know that because it is on the line.

The distance formula gives you .