Given that the line y = mx + c is a tangent to the curve y = fx
, show that 4c = m2 − 12m + 16.

find constant c2:55 pmfor which the line 4y = 2x +c is tangent to the curve y=4x + 8/x

The tangent to the curve C: y=4x^2 at the point A is parallel to the straight line L: 2x-y+24=0. Find the equation of the tangent to C at A.

If m is the slope of the common tangent of the parabola y2 = 16x and the circle x2 + y2 = 8, then m2 is equal to :

Find the value of c such that y = x + c is a tangent to the parabola y = x2 − x − 12.Hint: Consider the discriminant of the resulting quadratic.b i Sketch the parabola with equation y = −2x2 − 6x + 2.ii Find the values of m for which the straight line y = mx + 6 is tangent to theparabola. Hint: Use the discriminant of the resulting quadratic.6 a Find the value of c such that the line with equation y = 2x + c is tangent to theparabola with equation y = x2 + 3x.

If  y  =  mx + c  is common tangent to  x225 + y24  =  1, x2 + y2  =  16  and  y2  =  4ax(a  >  0) , then which of the following can be TRUE?