Question

I don't know how to approach this question, please help!
Find the value of the constant c for which the line y=4x+c is a tangent to the curve y^2=4x

Answer 1

This is what I tried but it doesn't seem to be going anywhere.

Answer 2

@ganeshie8 help us out

Answer 3

so far so good

Answer 4

\(16x^2-4x =-8xc-c^2 \)

rearrange the equation in standard form
\(16x^2+x(8c-4) + c^2 = 0\)

For the line to be a tangent, you want the discriminant to be \(0\) :
\((8c-4)^2 - 4*16*c^2=0\)

solve \(c\)

Answer 5

I am a bit confused with how you rearranged it.

Answer 6

How did you decide to put those numbers in the brackets?

Answer 7

I wanted to see a quadratic in \(x\), so arranged it in decreasing exponent of \(x\)

Answer 8

Notice that the equation is in form \(ax^2+bx+c=0\)

Answer 9

Ok, I think I understand better now. So if I started working on it from that last line I would be going in the right direction with it?

Answer 10

Yes

Answer 11

Thank you!

Answer 12

yw