Posted by **Aparna** on Friday, January 25, 2013 at 9:44pm.

Given the curve x^2-xy+y^2=9

A) write a general expression for the slope of the curve.

B) find the coordinates of the points on the curve where the tangents are vertical

C) at the point (0,3) find the rate of change in the slope of the curve with respect to x

I don't even know where to start!! Please help!

- Ap calc.. Dying!! Please help! -
**Reiny**, Friday, January 25, 2013 at 11:14pm
A)

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

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

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

B) for a vertical tangent dy/dx is undefined

For that to happen , the denominator has to be zero

2y - x = 0

or x = 2y

sub back into original:

(2y)^2 - (2y)(y) + y^2 = 9

4y^2 - 2y^2 + y^2 = 9

3y^2 = 9

y^2 = 3

y = ± √3

if y =+√3 , then x = 2√3 ---> point (2√3, √3)

if y = -√3 , then x = -2√3 ---> point (-2√3, -√3)

C) at (0,3)

dy/dx = (3 - 0)/(6-0) = 1/2

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