Equivalent Cartesian Equation of Parametric Equations
Problem
Find the Cartesian equation of the curve represented by $x = 4t + 3$ and $y = 16t^2 - 9$, -∞ < t < +∞.
| A. $y = x^2 + 6x$ | C. $y = x^2 + 4x$ |
| B. $y = x^2 - 6x$ | D. $y = x^2 - 4x$ |
Parametric Equations
Find y’ if x = 2 arccos 2t and y = 4 arcsin 2t
Problem
Find y’ if x = 2 arccos 2t and y = 4 arcsin 2t.
| A. 2 | C. 4 |
| B. -2 | D. -4 |
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Slope of a Curve of Given Parametric Equations
Problem
A point moves in the plane according to equations x = t2 + 2t and y = 2t3 - 6t. Find dy/dx when t = 0, 2, 5.
| A. -3, -3, -12 | C. 3, 3, 12 |
| B. 3, -3, 12 | D. -3, 3, 12 |
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Cycloid: equation, length of arc, area
Problem
A circle of radius r rolls along a horizontal line without skidding.
- Find the equation traced by a point on the circumference of the circle.
- Determine the length of one arc of the curve.
- Calculate the area bounded by one arc of the curve and the horizontal line.
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