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

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

anonymous · Answer

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

rock_mit182 · Answer

@ganeshie8  help us out

ganeshie8 · Answer

so far so good

ganeshie8 · Answer

$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 $c$

anonymous · Answer

I am a bit confused with how you rearranged it.

anonymous · Answer

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

ganeshie8 · Answer

I wanted to see a quadratic in $x$, so arranged it in decreasing exponent of $x$

ganeshie8 · Answer

Notice that the equation is in form $ax^2+bx+c=0$

anonymous · Answer

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?

ganeshie8 · Answer

Yes

anonymous · Answer

Thank you!

ganeshie8 · Answer

yw