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
Answered by Francesca T. Maths tutor

3103 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Express the following in partial fractions: (x^2+4x+10)/(x+3)(x+4)(x+5)


Using the addition formula for sin(x+y), find sin(3x) in terms of sin(x) and hence show that sin(10) is a root of the equation 8x^3 - 6x + 1


find the value of x for when f(x)=0. f(x)=9x^(2)-4


Given that: y = 5x^3 + 7x + 3. What is dy/dx? What is d^2y/dx^2?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning