# Math Help - analytic geometry (circles)

1. ## analytic geometry (circles)

Find the equation of the circle of radius $\sqrt{5}$ tangent to the line 2x+y-3=0 and having its center on the line 2x+3y = 4.

2. ## Re: analytic geometry (circles)

Originally Posted by TechnicianEngineer
Find the equation of the circle of radius $\sqrt{5}$ 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 $(p,q)\in~2x+3y=4$ having distance of $\sqrt{5}$ from $2x+y-3=0$.

3. ## Re: analytic geometry (circles)

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)

4. ## Re: analytic geometry (circles)

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 $2p+3q=4$ because it is on the line.

The distance formula gives you $\frac{|2p+q-3|}{\sqrt{2^2+1^2}}=\sqrt{5}$.