Given a fixed parabola and a family of parallel lines with given fixed gradient, find the one line that intersects the parabola in one single point
Let the parabola be y=x2 and let the family of lines be y=2x+c, in order to study the intersection points we need to consider the second order linear system given by having the two equations above. Hence, we get x2 -2x-c=0 and this equation has one single solution if and only if -c=1.
Therefore, the solution line is y=2x-1
FT
Related Maths A Level answers
All answers ▸I don't understand how to visualise differentiation, please could you show my an example to allow me to understand what it actually is better?
given that y = 1 when x = π, find y in terms of x for the differential equation, dy/dx = xycos(x)
Show that r^2(r + 1)^2 - r^2(r - 1)^2 ≡ 4r^3.
How do I find dy/dx for a given equation, once this is found how do I find the value of x such that dy/dx = 0.