Posted by **Jen** on Monday, October 16, 2006 at 8:53am.

Find normals to the curve xy+2x-y=0 that are parallel to the line 2x+y=0

I have the answer: at(-1,-1), y=-2x-3, and at (3,-3), y=-2x+3

How do we get this? Thanks.

xy + 2x - y=0

x dy/dx + y + 2 - dy/dx=0

dy/dx (x-1)= -y-2

dy/dx= - (y+2)/(x-1)

The normal to this has a slope of

(x-1)/(y+2)

but this has to be parallel to a slope of -2

(x-1)/(y+2) = -2

x-1= -2y -4

x= -(2y +3 ) and the x,y has to be on the

curve xy + 2x - y=0 ,or

(-(2y +3 )y) + 2(-(2y +3 )) - y=0

-2y^2-3y -4y-6-y=0

2y^2 + 8y + 6=0

y^2 + 4y +3=0

(y+3)(y+1)=0

and you have your two y solutions, put these back into the original equation to get the x values.

Sorry about the transcription error in the first post. Thanks for catching it.

## Answer This Question

## Related Questions

- Calculus - How do I find the normals to the curve xy+ 2x - y = 0 that are ...
- Calculus-implicit differentiation - How do I find the normals to the curve xy+ ...
- Calculus - Find the normals to the curve xy + 2x - y = 0 that are parallel to ...
- Calculus - Find the normals to the curve xy + 2x - y = 0 that are parallel to ...
- math - The parametric equations of a curve are x = 4t and y = 4 − t2. Find...
- Maths (Tangents and Normals) - find the points on the curve [(x^2 )+ (y^2) = 18...
- 12th Grade Calculus - 1. a.) Find an equation for the line perpendicular to the ...
- math - the curve y=x^2 - 3x - 4 cross the x-axis at P and Q. the tangent to the ...
- math - the curve y=x^2 - 3x - 4 cross the x-axis at P and Q. the tangent to the ...
- calculus - Find the point on the curve y=1 x2+14 x such that the tangent line to...

More Related Questions