Parametric Equations in Algebraic Contexts
Math ⇒ Algebra
Parametric Equations in Algebraic Contexts starts at 11 and continues till grade 12.
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Convert the parametric equations x = 4t + 2, y = 3t - 1 to a Cartesian equation.
Given the parametric equations x = 2t + 1, y = t², for what value(s) of t does y = 9?
Given the parametric equations x = t + 1, y = 2t - 3, find the coordinates of the point when t = 4.
Given x = 2 cos t, y = 2 sin t, what is the radius of the circle represented by these equations?
Given x = 2t + 3, y = 4t - 5, find the value of t when x = 7.
Given x = 2t, y = 3t + 1, find the Cartesian equation relating x and y.
Given x = 2t, y = t², what is the Cartesian equation relating x and y?
Given x = 4 cos t, y = 3 sin t, what is the equation of the ellipse in Cartesian form?
Which of the following is a correct parametric representation for the hyperbola x² - y² = 1?
(1) x = cosh t, y = sinh t
(2) x = t, y = t²
(3) x = cos t, y = sin t
(4) x = t, y = 1/t
Which of the following is a correct parametric representation for the parabola y = x²?
(1) x = t, y = t²
(2) x = t², y = t
(3) x = t, y = 2t
(4) x = t, y = t³
Which of the following is a parametric equation for a circle of radius r centered at the origin?
(1) x = r cos t, y = r sin t
(2) x = r t, y = r t
(3) x = r + t, y = r - t
(4) x = t², y = t³
Which of the following is a parametric equation for a line passing through (1, 2) with direction vector (3, 4)?
(1) x = 1 + 3t, y = 2 + 4t
(2) x = 3t, y = 4t
(3) x = 1 + t, y = 2 + t
(4) x = 3 + t, y = 4 + t
Fill in the blank: The parameter in parametric equations is usually denoted by ______.
Fill in the blank: The parametric equations x = a cos t, y = a sin t, z = bt represent a ______ in three-dimensional space.
Fill in the blank: The parametric equations x = a cos t, y = b sin t represent an ______.
Fill in the blank: The parametric equations x = t, y = t² - 4t + 3 represent a parabola with vertex at (______, ______).
True or False: Eliminating the parameter from parametric equations always results in a function y = f(x).
True or False: Parametric equations can be used to describe motion in three dimensions.
True or False: The parametric equations x = 2t + 1, y = 3t - 4 represent a straight line in the xy-plane.
True or False: The parametric equations x = 2t, y = 2t represent a line passing through the origin.
