My brother and I have been working on this problem for the better part of the day. I think we keep overlooking something. Please help us with this problem.
Normals parallel to a line: Find the normals to the curve xy+2x-y=0 that are parallel to the line 2x+y=0.
Thank you in advance for your responces.
Ok, I see what you did. I kept differentiating implicity and I must have been overlooking a mistake (even though it should have worked too). But I came up with y=-2x+3 , y=-2x-3 as the equations of my normals. Everything looks good when I graph it too, so I think this is right. Thank you very much for your quick responce and your help.
You should get the x-coordinates of the required points on the given curve are x = 3 and x = -1.
Edit: Reckoner, you should have posted your reply!
Therefore you require
Since the points on the curve that the required normals pass through obviously lie on the curve, you also require
Solve equations (1) and (2) simultaneously:
x = 3 and y = -3 or x = -1 and y = -1.
Equation of normal 1: m = -2 and passes through the point (3, -3). .
Equation of normal 2: m = -2 and passes through the point (-1, -1). .