Calculus 1

The curve with the equation y^2=5x^4-x^2 is called a kampyle of Eudoxus. Find an equation of the tangent line to this curve at the point (-1,2).

1. 👍
2. 👎
3. 👁
1. y^2=5x^4-x^2

2y dy/dx = 20x^3 - 2x
dy/dx = (20x^3 - 2x)/(2y)
= (10x^3 - x)/y
at (-1,2)
dy/dx = (-10+1)/2
= -9/2

so the tangent equation is 9x + 2y = c
with (-1,2) lying on it, so
-9 + 4 = c = -5

the tangent equation is 9x + 2y = -5

check:
http://www.wolframalpha.com/input/?i=y%5E2%3D5x%5E4-x%5E2+%2C+9x+%2B+2y+%3D+-5+%2C+from+-2+to+0

1. 👍
2. 👎
2. nope that is incorrect
the tangent equation is -9/2x-5/2

1. 👍
2. 👎
3. First of all -9/2x-5/2 is NOT an equation

if you meant y = -(9/2)x - 5/2
then by golly, that is what my equation is

9x + 2y = -5
2y = -9x - 5
divide each term by 2

y = (-9/2)x - 5/2

1. 👍
2. 👎
4. well the online homework system didn't take it as a complete equation because the y= part was already outside of the answer box

1. 👍
2. 👎
5. well, there you go, how about that

1. 👍
2. 👎
6. It worked for mine, thanks Reiny.

1. 👍
2. 👎

Similar Questions

1. Calculus

Consider the curve given by y^2 = 2+xy (a) show that dy/dx= y/(2y-x) (b) Find all points (x,y) on the curve where the line tangent to the curve has slope 1/2. (c) Show that there are now points (x,y) on the curve where the line

2. calculus

1. Given the curve a. Find an expression for the slope of the curve at any point (x, y) on the curve. b. Write an equation for the line tangent to the curve at the point (2, 1) c. Find the coordinates of all other points on this

3. last calc question, i promise!

given the curve x + xy + 2y^2 = 6... a. find an expression for the slope of the curve. i got (-1-y)/(x + 4y) as my answer. b. write an equation for the line tangent to the curve at the point (2,1). i got y = (-1/3)x + (5/3). but i

4. Math

Find an equation of the curve that satisfies the given conditions: (d^2y/dx^2)=6x, the line y=5-3x is tangent to the curve at x=1

1. calculus 1

The point P(2,-1) lies on the curve y=1/(1-x) If Q is the point (x, 1/(1-x) find slope of secant line. these are the points 2, -1 1.5,2 1.9,1.111111 1.99,1.010101 1.999,001001 2.5,0.666667 2.1,0.909091 2.01,0.990099 2.001,0.999001

2. Mathematics

The gradient of a curve is defined by dy/dx = 3x^(1/2) - 6 Given the point (9, 2) lies on the curve, find the equation of the curve

3. AP AB Calculus

Linear approximation: Consider the curve defined by -8x^2 + 5xy + y^3 = -149 a. find dy/dx b. write an equation for the tangent line to the curve at the point (4,-1) c. There is a number k so that the point (4.2,k) is on the

4. calculus

Consider the curve given by the equation y^3+3x^2y+13=0 a.find dy/dx b. Write an equation for the line tangent to the curve at the point (2,-1) c. Find the minimum y-coordinate of any point on the curve. the work for these would

1. Math

The line has equation y=2x+c and a curve has equation y=8-2x-x^2. 1) for the case where the line is a tangent to the curve, find the value of the constant c. 2) For the case where c = 11, find the x-coordinates of the points of

2. Calculus

a)The curve with equation: 2y^3 + y^2 - y^5 = x^4 - 2x^3 + x^2 has been linked to a bouncing wagon. Use a computer algebra system to graph this curve and discover why. b)At how many points does this curve have horizontal tangent