The line with equation mx- y-3=0 touches the circle with equation x²- 4x + y² - 6y = 7. Find the two possible values of m.
The line will touch the circle (is a tangent) when there is a single point of intersection, so solve the simultaneous equations and use the discriminant to determine the values of m.
y=mx-3 x2 -4x+(mx-3)2 -6(mx-3)=7 I can just help you to it .Because you didn't tell me is the line tangent or not. If you know that you can use delta to solve it. Have a nice day