calculus
posted by Lee .
the curve with equation 2(x^2+y^2)^2=9(x^2y^2) is called a lemniscate. find the points on the lemniscate where the tangent is horizontal.

calculus 
Steve
just plug and chug:
4(x^2 + y^2)(2x + 2yy') = 9(2x  2yy')
Now, the tangent is horizontal when y' = 0
4(x^2 + y^2)(2x) = 9(2x)
8x^3 + 8xy^2 = 18x
2x(4x^2 + 4y^2  9) = 0
So, either x=0
substitute back into original equation:
2y^4 = 9y^2
y=0
or,
4x^2 + 4y^2 = 9
x^2 = (9  4y^2)/4
Substitute that back into the original equation
2((9  4y^2)/4 + y^2)^2 = 9((9  4y^2)/4  y^2)
Expand the binomial and solve for y^2 
calculus 
Kelvin
Tan^3(xy^2+y)=x
Use derivative 
calculus 
Kelvin
Find .... Tan^3(xy^2+y)=x
Use derivative
Respond to this Question
Similar Questions

Calculus
Find the equation of the tangent line to the curve (a lemniscate) 2(x^2+y^2)^2 = 25(x^2y^2) at the point ( 3 , 1 ) 
Calculus  Verify?
Find the slope of the tangent line to the curve (a lemniscate) 2(x^2+y^2)^2 = 25(x^2y^2) it is at pt (3,1) 
Calculus
Consider the curve y^2+xy+x^2=15. What is dy/dx? 
calculus
the lemniscate revolves about a tangent at the pole find sufaces of the solid generated? 
Calculus
Please help this is due tomorrow and I don't know how to Ive missed a lot of school sick Consider the curve given by the equation x^3+3xy^2+y^3=1 a.Find dy/dx b. Write an equation for the tangent line to the curve when x = 0. c. Write … 
Calculus. I need help!
HARDER PARTS WAS 3(x^2+y^2)^2=26(y^2+y^2) Find the equation of the tangent line to the curve (a lemniscate) 3(x^2+y^2)^2=26(y^2+y^2) at the point (4,2). The equation of this tangent line can be written in the form y=mx+b where m is:? 
Math
(x^2+y^2)^2=4(x^2y^2) Equation of a lemniscate curve 
Calculus
Find the slope of the tangent line to the curve (a lemniscate) 2(x^2+y^2)^2 = 25(x^2y^2) at point (3,1). 
MathCalc
Find an equation of the tangent line to the curve 2(x2+y2)2=25(x2−y2) (a lemniscate) at the point (3,1). Please help. 
Calculus
Find the points on the lemniscate, given below, where the tangent is horizontal 2(x^2 + y^2)^2 = 49(x^2 − y^2)