SOLUTION: The line mx-y=0 is tangent to the circle X2+Y2-6X+2y+2=0 find the two values of m.

Question 602433: The line mx-y=0 is tangent to the circle X2+Y2-6X+2y+2=0 find the two values of m.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
If the line <--> is tangent to the circle, they have only one point in common. So, substituting
into the equation for the circle,
, there should be only one point that is a solytion.
That would mean only one pair (x,y), meaning only one value for x.
So, here we go
--> -->
If a quadratic equation has only one solution its discriminant must be zero:

For the equation with m,
, and
The discriminant is
--> --> -->
Dividing both sides of the equal sign by (-4), we get as much friendlier equation:

and factoring, we get
with solutions and .

RELATED QUESTIONS
Find the equation of the line tangent to a circle x2 + y2 = 13 at... (answered by josgarithmetic)

A circle has equation x^2+y^2-2x+4y-15=0 Find the values for which the line mx+2y-7=0... (answered by Alan3354)

Find the equation of the line tangent to the circle x2 + y2 = 25 at point... (answered by Fombitz,htmentor,Boreal,ikleyn,MathTherapy)

Find the equation of the tangent line to the circle whose equation is x2 + y2 - 18x +... (answered by lwsshak3)

For what values of m is the line y= mx a tangent to the parabola y=x^2 - 8x +... (answered by ikleyn)

The homework question is,Show that the line with equation y=2x-10 is a tangent to the... (answered by scott8148)

The line with the equation y=mx+c is tangent to the circle with equation x^2+y^2=36. Find (answered by josgarithmetic)

Find the equation of the circle concentric with the circle x2+y2+6x-10y+33=0 and touching (answered by Alan3354)

a line y=c-3x is the tangent to a circle: x^2+y^2-4x-2y-5=0. What are the values of... (answered by oscargut)