Thread: The equation of the normal to a curve which is parallel to a given line

this is the question:

find the equation of the normal to the curve y=3+2x-x^2 which is parallel to the line 2y-x-3=0

please help me...i dont know how to do..

Originally Posted by mastermin346

this is the question:

find the equation of the normal to the curve y=3+2x-x^2 which is parallel to the line 2y-x-3=0

please help me...i dont know how to do..

The gradient of 2y-x-3=0 is 1/2. Therefore the gradient of the required normal is 1/2 therefore the gradient of the tangent is -2. So solve dy/dx = -2 to get the x-coordinate and hence y-coordinate of the required point on the curve. Now you have a point and you have a gradient and therefore you can write down the equation of the normal line.

Originally Posted by mr fantastic

The gradient of 2y-x-3=0 is 1/2. Therefore the gradient of the required normal is 1/2 therefore the gradient of the tangent is -2. So solve dy/dx = -2 to get the x-coordinate and hence y-coordinate of the required point on the curve. Now you have a point and you have a gradient and therefore you can write down the equation of the normal line.

can u write it?it dificult to me.

Originally Posted by mastermin346

this is the question:

find the equation of the normal to the curve y=3+2x-x^2 which is parallel to the line 2y-x-3=0

please help me...i dont know how to do..

i am sure you know that the gradient of is 1/2



... gradient of tangent

so gradient of normal will be

have it equal to 1/2 . Do you know why ?

then solve for x , sub into the original equation to get y.

After that , make use the formula that i gave you in my post tp your other question to get the equation .

Originally Posted by mastermin346

can u write it?it dificult to me.

You have spent no more than 8 minutes thinking about what I posted before aksing for more help. You need to spend more time than that thinking about the question and the reply I gave.

Have you tried doing what I suggested? What don't you understand? Where do you get stuck?