Posted by **Lee** on Sunday, October 30, 2011 at 8:40pm.

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

- calculus -
**Steve**, Monday, October 31, 2011 at 11:50am
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**, Saturday, January 26, 2013 at 5:36pm
Tan^3(xy^2+y)=x

Use derivative

- calculus -
**Kelvin**, Saturday, January 26, 2013 at 5:40pm
Find .... Tan^3(xy^2+y)=x

Use derivative

## Answer this Question

## Related Questions

- Calculus - Find the equation of the tangent line to the curve (a lemniscate) 2(x...
- Calculus. I need help! - HARDER PARTS WAS 3(x^2+y^2)^2=26(y^2+y^2) Find the ...
- Calculus - Find the slope of the tangent line to the curve (a lemniscate) 2(x^2+...
- Calculus - Verify? - Find the slope of the tangent line to the curve (a ...
- calculus - the lemniscate revolves about a tangent at the pole find sufaces of ...
- Math - (x^2+y^2)^2=4(x^2-y^2) Equation of a lemniscate curve
- Calculus - Please help this is due tomorrow and I dont know how to Ive missed a ...
- Calculus - Consider the curve y^2+xy+x^2=15. What is dy/dx? Find the two points ...
- Calculus - a)The curve with equation: 2y^3 + y^2 - y^5 = x^4 - 2x^3 + x^2 has ...
- Implicit Differentiation - Find the slope of the tangent line to the curve (a ...