Math Help - pre-calculus question with circle

1. pre-calculus question with circle

The circle x2+y2-4x-6y+k=0 touches the x axis at the point t. Find the value of k and the coordinates of t.
I got square root of 52-k for the radius but dont know what to do next.

2. Dear milan,

the equation of normal unit circle is:
x^2 + y^2 = 1.

The general circle can have other radius, can shift along x-axis and along y-axis, so the equation of general circle is:
(x-a)^2 + (y-b)^2 = r^2.

I suggest you that convert the original equation to such form and all will be happy.

I think sqrt(52) is false result.

3. Circle touching x-axis

Hello milan
Originally Posted by milan
The circle x2+y2-4x-6y+k=0 touches the x axis at the point t. Find the value of k and the coordinates of t.
I got square root of 52-k for the radius but dont know what to do next.

The circle intersects the x-axis where y = 0. So put y = 0 in the equation and you get:

$x^2 - 4x \dots$

This is a quadratic equation in x. If the circle touches the x-axis, it must have equal roots. So? Can you see what to do next?