# Thread: Tangent & Normal (Q8b)

1. ## Tangent & Normal (Q8b)

The tangent and the normal to the curve $\displaystyle y=4(\sqrt{x+2})$ at the point P(7,12) cut the x-axis at point M and N respectively. Calculate the area of the Triangle PMN.

I am aware that I have to find the equation of the tangent and the normal. However, I seem to not be able to get them correctly... The problem lies with getting the equation of the tangent and normal. Calculating the area of the triangle should be fine, so I require no help in it.

I would be grateful if someone would show me the detailed workings on getting the equations of tangent and normal, thanks!

2. Originally Posted by Punch
The tangent and the normal to the curve $\displaystyle y=4(\sqrt{x+2})$ at the point P(7,12) cut the x-axis at point M and N respectively. Calculate the area of the Triangle PMN.

I am aware that I have to find the equation of the tangent and the normal. However, I seem to not be able to get them correctly... The problem lies with getting the equation of the tangent and normal. Calculating the area of the triangle should be fine, so I require no help in it.

I would be grateful if someone would show me the detailed workings on getting the equations of tangent and normal, thanks!
first of all , differentiate to find the gradient of tangent .

$\displaystyle \frac{dy}{dx}=\frac{2}{\sqrt{x+2}}$

and at (7,12) , $\displaystyle \frac{dy}{dx}=\frac{2}{\sqrt{7+2}}=2/3$

equation of tangent : y-12=(2/3)(x-7)

3. I think I found the problem now... I didn't sub value of x into the $\displaystyle \frac{dy}{dx}$ thanks!