Problem
Find the Cartesian equation of the curve represented by x=4t+3 and y=16t2−9, -∞ < t < +∞.
| A. y=x2+6x | C. y=x2+4x |
| B. y=x2−6x | D. y=x2−4x |
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. x2+y2+z2−9=0 |
| B. x2+y2+z2−6x−6y−6z+18=0 |
| C. x2+y2+z2−4x−4y−4z+12=0 |
| D. x2+y2+z2−8x−8y−8z+14=0 |
Problem
Calculate the area enclosed by the curve x2+y2−10x+4y−196=0.
| A. 15π | C. 169π |
| B. 13π | D. 225π |
Problem
A circle has an equation of x2+y2+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 x2+y2=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 x2+y2−6x=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 |
