posted by Allison on .
Find a Cartesian equation relating and corresponding to the parametric equations: x=2sin(3t), y=9cos(3t).
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 y^2 is 4.
b)Find the equation of the tangent line to the curve at the point corresponding to t=pi/9
square each equation
divide by coefficient of RHS and add:
Multiply by 4*81 to have common denominator of 1
To find tangent, calculate dy/dx=y'(x,y) using implicit differentiation.
dy/dx at t0=pi/9:
evaluate m=y'(2sin(3t0), 9cos(3t0))
Equation of tangent line:
L : (y-9cos(3t0))=m(x-2sin(3t0))