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
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
Answer this Question
More Related Questions
- calculus - 1. Given the curve a. Find an expression for the slope of the curve ...
- last calc question, i promise! - given the curve x + xy + 2y^2 = 6... a. find an...
- 12th Grade Calculus - 1. a.) Find an equation for the line perpendicular to the ...
- Calculus - Please help this is due tomorrow and I dont know how to Ive missed a ...
- math - A curve has implicit equation x^2-2xy+4y^2=12 a)find the expression for ...
- please help; calc - original curve: 2y^3+6(x^2)y-12x^2+6y=1 dy/dx=(4x-2xy)/(x^2+...
- calculus - there are two tangents lines to the curve f(x) = 3x^2 that pass ...
- Calculus - Consider the curve given by y^2 = 2+xy (a) show that dy/dx= y/(2y-x...
- Calc. - sketch the curve using the parametric equation to plot the points. use ...
- calculus - Consider a plane curve which is described in polar coordinates (r...