I'm really stuck on this maths question and don't know how to work it out. The question is y= -3x+c is a tangent to the circle x^2+y^2-4x-2y-5=0. Find c. Can anyone help? Thanks
I'm really stuck on this maths question and don't know how to work it out. The question is y= -3x+c is a tangent to the circle x^2+y^2-4x-2y-5=0. Find c. Can anyone help? Thanks
Substitute y=x+c into the equation of the circle and rearrange to get a quadratic equation set to 0. Then as the line is a tangent to the curve, the discriminant will be 0. So if you do b^2 -4ac which is the discriminant and set it =0 you will form a quadratic in terms of c and so you can then solve.
thank you so much :-). I subbed the equation of a line into the equation of the circle and got 10x^2-6cx+c^2+2x+c-5 but am not sure what would be a,b,c?
thank you so much :-). I subbed the equation of a line into the equation of the circle and got 10x^2-6cx+c^2+2x+c-5 but am not sure what would be a,b,c?
If you factorise for each term x^2, x and the constant term, you would get (assuming what you have written is correct) 10x^2 +2(1-3)x+c^2+c-5=0
I'm really stuck on this maths question and don't know how to work it out. The question is y= -3x+c is a tangent to the circle x^2+y^2-4x-2y-5=0. Find c. Can anyone help? Thanks