# normal line to the curve

• May 25th 2010, 06:26 PM
mastermin346
normal line to the curve
A curve $\displaystyle y=f(x)$ with the gradient function $\displaystyle \frac{dy}{dx}=\frac{x^2}{3x-1}.$

The straight line $\displaystyle ky=2x-7$ is normal to the curve $\displaystyle y=f(x)$ at $\displaystyle (2,m)$.Find the value of $\displaystyle k$ and $\displaystyle m$.

any help will appreciate,.
• May 25th 2010, 07:00 PM
mr fantastic
Quote:

Originally Posted by mastermin346
The straight line $\displaystyle ky=2x-7$ is normal to the curve $\displaystyle y=f(x)$ at $\displaystyle (2,m)$.Find the value of $\displaystyle k$ and $\displaystyle m$.

any help will appreciate,.

There is not enough information given. Go back and check the question.
• May 25th 2010, 07:07 PM
mastermin346
Quote:

Originally Posted by mr fantastic
There is not enough information given. Go back and check the question.

hi sir..

sorry,my mistake

the question is. A curve $\displaystyle y=f(x)$ with gradient function $\displaystyle \frac{dy}{dx}=\frac{x^2}{3x-1}$.
• May 25th 2010, 07:26 PM
pickslides
Well start by substituting $\displaystyle x=2$ into $\displaystyle \frac{dy}{dx}$ what you you get? What does that mean?
• May 25th 2010, 07:31 PM
mastermin346
Quote:

Originally Posted by pickslides
Well start by substituting $\displaystyle x=2$ into $\displaystyle \frac{dy}{dx}$ what you you get? What does that mean?

hi,i get $\displaystyle \frac{dy}{dx}=\frac{4}{5}$ then?it mean the gradient right?
• May 25th 2010, 07:42 PM
pickslides
Quote:

Originally Posted by mastermin346
hi,i get $\displaystyle \frac{dy}{dx}=\frac{4}{5}$ then?it mean the gradient right?

Correct, it is the gradient of $\displaystyle f(x)$ at $\displaystyle x=2$. Now what is the relationship between the gradient and the normal?

Hint: $\displaystyle m_N\times m_T = -1$

How can we use this value?
• May 25th 2010, 08:01 PM
mastermin346
Quote:

Originally Posted by pickslides
Correct, it is the gradient of $\displaystyle f(x)$ at $\displaystyle x=2$. Now what is the relationship between the gradient and the normal?

Hint: $\displaystyle m_N\times m_T = -1$

How can we use this value?

i get the gradient of normal is $\displaystyle -\frac{5}{4}$.
• May 25th 2010, 08:32 PM
pickslides
Quote:

Originally Posted by mastermin346

The straight line $\displaystyle ky=2x-7$ is normal to the curve $\displaystyle y=f(x)$ at $\displaystyle (2,m)$.

so maybe its' time to find $\displaystyle k$

Making the form $\displaystyle y=mx+c$

$\displaystyle ky=2x-7\implies y=\frac{2}{k}x-\frac{7}{k}$

$\displaystyle \frac{-5}{4}= \frac{2}{k}$