1. ## Find parabola if...

Q: Find the equation of the parabola if its tangent line at x=2 is

$\displaystyle y=\frac{2}{\sqrt{3}}x-\frac{\sqrt{3}}{3}$

TYIA

2. Originally Posted by hello
Q: Find the equation of the parabola if its tangent line at x=2 is

$\displaystyle y=\frac{2}{\sqrt{3}}x-\frac{\sqrt{3}}{3}$
There are quite a few parabolas that will work ... is there more information? what do the instructions for this exercise say?

3. Originally Posted by hello
Q: Find the equation of the parabola if its tangent line at x=2 is

$\displaystyle y=\frac{2}{\sqrt{3}}x-\frac{\sqrt{3}}{3}$

TYIA
At x= 2 y= $\displaystyle \sqrt{3}$ so you are asking for a parabola that passes through $\displaystyle (2,\sqrt{3})$ and has derivative $\displaystyle \frac{2}{\sqrt{3}}$ there. As skeeter says, there are an infinite number of such parabolas. Even if we restrict to parabolas with vertical axis, there are an infinite number of answers.

4. Oops, I did leave out some info. Sorry, hehe I kinda started off in the middle of the question.

Original q: Find equation of a parabola which is tangent to this curve

$\displaystyle y=\sqrt{x^2-1}$ at x=2

so yeah this

was just the tang. line I found for the given function.

5. solved nvm

thanks

6. $\displaystyle \sqrt{x^2-1} = ax^2+bx+c$ at $\displaystyle x = 2$

derivatives ...

$\displaystyle \frac{x}{\sqrt{x^2-1}} = 2ax + b$

... are also equal at $\displaystyle x = 2$.

since the question said "a" parabola, let $\displaystyle c = 0$.

get two equations in terms of $\displaystyle a$ and $\displaystyle b$ and solve the system for the coefficients.

7. Thanks, yeah I realised I had to do something like that so I took the even easier route of letting b=0 and therefore finding a and c.