Homework SourseFind a Cartesian equation relating and corresponding to the
Find a Cartesian equation relating and corresponding to the parametric equations
x=4t/(1+t^3) y=(3t^2)/(1+t^3)
Write your answer in the form
P(x,y)=0
where P(x,y) is a polynomial in x and y such that the coefficient of x^3 is 27.
Answer:
Find the equation of the tangent line to the curve at the point corresponding to t=1.
Answer:
x=4t/(1+t^3) y=(3t^2)/(1+t^3)
Write your answer in the form
P(x,y)=0
where P(x,y) is a polynomial in x and y such that the coefficient of x^3 is 27.
Answer:
Find the equation of the tangent line to the curve at the point corresponding to t=1.
Answer:
Solution
let k = t/(1+t^3) x = 4k, y = 3tk y = 3xt/4 t = 4y/3x x = 4(4y/3x)/(1 + 64y^3/27x^3) x = (16/3x)(27x^3/(27x^3 + 64y^3) 144x = 27x^3 + 64y^3 27x^3 + 64y^3 - 144x = 0 at t=1,x = 2, y = 3/2 81x^2 + 192y^2y\' -144 = 0 81(4) + 432y\' - 144 = 0 y\' = -0.417 equation of tangent line is y-1.5 = -0.417(x-2) 0.417x +y -0.67 = 0
