Homework Help: Ap calc.. Dying!! Please help!

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 = ą √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

Related Questions

last calc question, i promise! - given the curve x + xy + 2y^2 = 6... a. find an...
calculus - 1. Given the curve a. Find an expression for the slope of the curve ...
please help; calc - original curve: 2y^3+6(x^2)y-12x^2+6y=1 dy/dx=(4x-2xy)/(x^2+...
12th Grade Calculus - 1. a.) Find an equation for the line perpendicular to the ...
Help Calc.! - original curve: 2y^3+6(x^2)y-12x^2+6y=1 dy/dx=(4x-2xy)/(x^2+y^2+1...
Ap Calc AB - Find the equation of the line tangent to the curve at (5, -3) (x-2...
Calc - Hi! Please help :-) Find an equation for the circle of the curvature of ...
Calculus ap - Use implicit differentiation to find the slope of the tangent line...
Calculus - Please help this is due tomorrow and I dont know how to Ive missed a ...
Calc - find the slope of the tangent to the curve: y^2=x^3/xy

For Further Reading

First Name:
School Subject:
Answer: