If you are an experienced mathematician please read.

[jamieneedshelp]

Ok i need soome major help here folks. Any help is appreciated. Thank you.

In this exercise you will find the slope of the line tangent to the porabola y=x^2 at the point P(a,a^2)

A)Write an equatioin in point slope form, of the line through point P with slope m.

B)Using your equation from part (a) to eliminate y in the equation of the parabola, write a quadratic equation involving x and m that must be satisfied by all points of intersection of any line through point P and the parabola.

C)Since a tangent line to a parabola intersects the graph only once, the equation you wrote must have exactly one solution for x. What does this tell you about the discriminant of the equation regarding x as the variable?

D)Write the discriminant of the equation in terms of m, and use your answer to part (c) to find m (i.e. the slope of the line tangent at P).

 

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[Dev2011]

Ok i need soome major help here folks. Any help is appreciated. Thank you.

In this exercise you will find the slope of the line tangent to the porabola y=x^2 at the point P(a,a^2)

A)Write an equatioin in point slope form, of the line through point P with slope m.

B)Using your equation from part (a) to eliminate y in the equation of the parabola, write a quadratic equation involving x and m that must be satisfied by all points of intersection of any line through point P and the parabola.

C)Since a tangent line to a parabola intersects the graph only once, the equation you wrote must have exactly one solution for x. What does this tell you about the discriminant of the equation regarding x as the variable?

D)Write the discriminant of the equation in terms of m, and use your answer to part (c) to find m (i.e. the slope of the line tangent at P).

For part A, I got y-a[sup:xc6vrg0j]2[/sup:xc6vrg0j]=m(x-a)

For part B, I set up a system of equations with y=x[sup:xc6vrg0j]2[/sup:xc6vrg0j] and y-a[sup:xc6vrg0j]2[/sup:xc6vrg0j]= m(x-a)

The quadratic equation I ended up with (which I'm really not positive IS a quadratic equation) is x[sup:xc6vrg0j]2[/sup:xc6vrg0j]-mx+ma-a[sup:xc6vrg0j]2[/sup:xc6vrg0j]=0

I'm hoping someone checks behind me on this..