find the equation of the tangent to the parabola y^2=4px perpendicular to the line 4y-x 3=0

1. Find the gradient of the line you were given.
2. Find the gradient of the tangent to the parabola using your answer to step 1.

Now there are two ways you can proceed, one using calculus and not the other. I'll move with the other for the time being.

3. Put the equation of the tangent like this: y = mx + c

where m is the gradient of the tangent and c is for you to find.

4. Now, you must find the point on the parabola which touches the line at a single point. So, equate the curve given with the equation of the tangent, use the fact that for them to meet a single point, b^2 - 4ac = 0 and solve for c in terms of p.

5. Put back that value into the equation of the tangent.

Do you think you understood everything? :)