Find the equation of the normal

**creatively12** · September 28th 2009, 03:03 PM

The tangent at P to the curve y=x^2 has gradient 3. Find the equation of the normal at P.

The answer of this question is 12y=-4x+33

Please help me with this question, please

**Danny** · September 28th 2009, 03:11 PM

Originally Posted by creatively12

The tangent at P to the curve y=x^2 has gradient 3. Find the equation of the normal at P.

The answer of this question is 12y=-4x+33

Please help me with this question, please

The slope of the tangent is given by $\frac{dy}{dx} = 2x$ . If this is 3 then the x value is $x = \frac{3}{2}.$ The normal has slope $- \frac{1}{3}$ . The equation for this through $\left( \frac{3}{2}, \frac{9}{4} \right)$ is

$<br /> y - \frac{9}{4} = - \frac{1}{3} \left(x- \frac{3}{2} \right)<br />$

and if you simplify you'll get the answer you give.

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