# analytic geometry (circles)

• Nov 28th 2011, 07:53 AM
TechnicianEngineer
analytic geometry (circles)
Find the equation of the circle of radius $\displaystyle \sqrt{5}$ tangent to the line 2x+y-3=0 and having its center on the line 2x+3y = 4.
• Nov 28th 2011, 07:58 AM
Plato
Re: analytic geometry (circles)
Quote:

Originally Posted by TechnicianEngineer
Find the equation of the circle of radius $\displaystyle \sqrt{5}$ 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 $\displaystyle (p,q)\in~2x+3y=4$ having distance of $\displaystyle \sqrt{5}$ from $\displaystyle 2x+y-3=0$.
• Nov 28th 2011, 08:09 AM
TechnicianEngineer
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)
• Nov 28th 2011, 08:19 AM
Plato
Re: analytic geometry (circles)
Quote:

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

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