How do you know what order to put the equation in? Does this affect the usage of the discriminant?
Can someone expand that equation and throw it on the other side to get the coefficient of x^2 positive and see what they get please.
I've done it.
Make the ys equal so 1/(x-2) = -x + k
Multiply both sides by (x-2): 1 = (x-2)(-x+k)
1 = -x^2 + kx + 2x -2k
x^2 + -kx - 2x + 2k + 1 = 0
x^2 -(k+2)x + 2k + 1 = 0
Then you have to use the discriminant, so b^2 - 4ac = (k+2)^2 - (4 * 1 * (2k+1)) = 0 (you're told it's a tangent, therefore only one POI, so the discriminant = 0), where a = 1, b = k+2, c = 2k+1. That bit threw me for a bit as I didn't realise the 2k + 1 was one term.
Multiply it all out and eventually you get k^2 - 4k = 0
I can't find the exact question but if you have a circle equation and the equation of a tangent, how do you find the equation of the other parallel tangent? Obviously you have the gradient but what point would you sub in? Thanks
I can't find the exact question but if you have a circle equation and the equation of a tangent, how do you find the equation of the other parallel tangent? Obviously you have the gradient but what point would you sub in? Thanks
I'm not sure if this is allowed BUT, if the tangent meets the circle at point (x,y), the other tangent parallel to it would meet the circle at point (-x,-y) because of the symmetry of circles. Now you have a point [(-x,-y)] and the gradient [same as the other one because they are parallel], so use y-y0=m(x-x0).
I'm not sure if this is allowed BUT, if the tangent meets the circle at point (x,y), the other tangent parallel to it would meet the circle at point (-x,-y) because of the symmetry of circles. Now you have a point [(-x,-y)] and the gradient [same as the other one because they are parallel], so use y-y0=m(x-x0).
Just did the exam. I thought that Section B was quite difficult. I have to rush it as I sent too long trying to perfect Section A. I am not great at mental artithematic so I though I'll take a long time on Section A. Even then I knew that I got one question wrong. I hope that this is the 4th time lucky but I doubt I will get anythig better than a D.