Find an Equation of the tangent line to the parabola at the given point and find the x-intercept of the line...

x^2=2y, (4,8)

- March 22nd 2011, 12:03 PMthelensbossFind an Equation of the Tangent Line to the parabola at the given point and find....
Find an Equation of the tangent line to the parabola at the given point and find the x-intercept of the line...

x^2=2y, (4,8) - March 22nd 2011, 12:12 PMpickslides
For

The tangent line is

The x-intercept can be found by making y=0 hence now solve for x - March 22nd 2011, 12:16 PMthelensboss
What is f' ?

- March 22nd 2011, 12:20 PMpickslides
- March 22nd 2011, 12:27 PMthelensboss
I haven't learned derivatives yet. Can you solve it like this:

Find the y-intercept by equating the lenths of the two sides of the isosceles triangle formed by the tangent line and the y-axis. (d1 and d2).

I just don't know how to equate them...

and then for slope you would do the slope formula - March 22nd 2011, 12:44 PMpickslides
- March 22nd 2011, 12:53 PMthelensboss
Alright thanks! But I still don't know how to find m with this? I just choose something? I guess I would use (4,8) and another point but what do I use?

- March 22nd 2011, 01:06 PMthelensboss
I need to solve this without CALC as I have not learned derivatives yet.

- March 22nd 2011, 04:57 PMskeeter
let be the equation of the tangent line thru the point

equation of the parabola is

the tangent line and the parabola have equal y-values ...

since the tangent line touches the curve at a single point, the resulting quadratic has a single solution ... the discriminant must = 0

choose the positive slope

... now you have the slope of the tangent line and can finish whatever it is you need to do.