# Thread: Find the equation of tangent and normal to the curve

1. ## Find the equation of tangent and normal to the curve

Question : Find the eq of tangent and normal to the curve
$\displaystyle y(x-2)(x-3)-x+7 = 0$
at the point where the curve meets the x-axis
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Solution:

$\displaystyle y = \frac{x-7}{x^2 - 5x +6 }$.............Is that correct?

$\displaystyle \therefore \frac{dy}{dx} = \frac{-x^2 + 14x -29}{(x^2 - 5x +6)^2}$...................Is that correct?????

2. Originally Posted by zorro
Question : Find the eq of tangent and normal to the curve
$\displaystyle y(x-2)(x-3)-x+7 = 0$
at the point where the curve meets the x-axis
-----------------------------------------------------------------
Solution:

$\displaystyle y = \frac{x-7}{x^2 - 5x +6 }$.............Is that correct?

$\displaystyle \therefore \frac{dy}{dx} = \frac{-x^2 + 14x -29}{(x^2 - 5x +6)^2}$...................Is that correct?????

differentiate (x - 7)/(x^2 - 5x + 6) - Wolfram|Alpha

You can do the simplifying of the Wolfram expression and see if it's equivalent to what you got.

3. ## what should i do nxt

Originally Posted by mr fantastic
differentiate (x - 7)/(x^2 - 5x + 6) - Wolfram|Alpha

You can do the simplifying of the Wolfram expression and see if it's equivalent to what you got.

$\displaystyle \frac{dy}{dx} = \frac{- (x^2 - 14x + 31)}{(x^2 - 5x + 6)^2}$
what should i do??????
Now eg of tangent is at $\displaystyle (x_0,y_0)$ is given by

$\displaystyle (y-y_0) = \frac{dy}{dx} (x-x_0)$

but i dont know $\displaystyle (x_0,y_0)$.................what should i do??????

4. Originally Posted by zorro
$\displaystyle \frac{dy}{dx} = \frac{- (x^2 - 14x + 31)}{(x^2 - 5x + 6)^2}$
what should i do??????
Now eg of tangent is at $\displaystyle (x_0,y_0)$ is given by

$\displaystyle (y-y_0) = \frac{dy}{dx} (x-x_0)$

but i dont know $\displaystyle (x_0,y_0)$.................what should i do??????
When the curve meets the x-axis, y = 0. Therefore $\displaystyle y_0 = 0$. To get $\displaystyle x_0$, solve $\displaystyle -x + 7 = 0$ (I hope you see why).