Calculus

Calculus of Parametric Equations

Parametric Equations - Tangent

         

Consider the polar curve rθ=6 r\theta = 6 . What is the slope of the tangent line of the polar curve at θ=π \theta = \pi ?

Given the curve x=12t,y=54t+2t2,x=1-2t, y=5-4t+2t^2, what is the equation of the tangent line to the curve at x=5?x=5 ?

For the curve given by x=9t1+t2,y=1t21+t2,x=\frac{9t}{1+t^2}, y=\frac{1-t^2}{1+t^2}, what is the equation of the tangent line to the curve for t=2?t=2 ?

Consider the polar curve r=22sinθ r = 22 \sin \theta . What is the slope of the tangent line at θ=π6 \theta = \frac{\pi}{6} ?

A curve is defined by (x,y)=(cos3θ,sin3θ)(x,y) =\left(\cos^3 \theta, \sin^3 \theta \right). If the equation for the tangent line at θ=23π\theta=\frac{2}{3}\pi is y=ax+by=ax+b, what is the value of a×b a \times b ?

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