Very confusing Parabola question?!?!? (1 Viewer)

[viviansidiss]

I just can't seem to figure out how to do this question. Can anyone please explain the answer (B=-5)

A parabola whose equation is in the form of y=Bx^2 (where B is a constant) has the line 20x - y + 20= 0 as a tangent. Find the value of B.

Thanks

 

[kaz1]

Simultaneously solve, find pt of intersection, sub in derivative.

 

[Aquawhite]

at above post.... the way to do it.

 

[Puttah]

ok so you have the two equations:

and

Take the derivative of each for their gradients:

and

Since the line is a tangent to the parabola at some point, their gradients are equal, thus ...

Now just substitute this result into the parabola equation:

and now sub this result into the line equation:

...

Hence,

 

[viviansidiss]

Cool thanks

 

[untouchablecuz]

alternatively, solve the equations simultaneously and you get the quadratic

Bx^2 - 20x - 20 = 0

discriminant = 400 + 80B

since the line is tangent, discriminant = 0

i.e. B = -5

 

[gurmies]

^ Better method imo