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. $y = x^2 - 4x$ |
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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. $y = x^2 - 4x$ |
Problem
Find the equation of a sphere of radius 3 and tangent to all three coordinate planes if the center is on the first octant.
A. $x^2 + y^2 + z^2 - 9 = 0$ |
B. $x^2 + y^2 + z^2 - 6x - 6y - 6z + 18 = 0$ |
C. $x^2 + y^2 + z^2 - 4x - 4y - 4z + 12 = 0$ |
D. $x^2 + y^2 + z^2 - 8x - 8y - 8z + 14 = 0$ |
Problem
Calculate the area enclosed by the curve $x^2 + y^2 - 10x + 4y - 196 = 0$.
A. 15π | C. 169π |
B. 13π | D. 225π |
Problem
A circle has an equation of $x^2 + y^2 + 2cy = 0$. Find the value of $c$ when the length of the tangent from (5, 4) to the circle is equal to one.
A. 5 | C. 3 |
B. -3 | D. -5 |
Problem
Calculate the acute angle between two intersecting surfaces whose equations are as follows:
$$2x - 4y - z = -5$$
$$3x + 4y + 5z = -6$$
A. 62.4° | C. 42.6° |
B. 64.2° | D. 46.2° |
Problem
What is the equation of the normal to the curve $x^2 + y^2 = 25$ at (4, 3)?
A. $4x + 3y = 0$ | C. $3x + 4y = 0$ |
B. $3x - 4y = 0$ | D. $4x - 3y = 0$ |
Problem
What is the radius of the circle $x^2 + y^2 - 6x = 0$?
A. 6 | C. 4 |
B. 9 | D. 3 |
Problem
Find the distance from the point A(1, 5, -3) to the plane 4x + y + 8z + 33 = 0.
A. 1/2 | C. 2/3 |
B. 2 | D. 1.5 |