Q. What is the family of curves represented by the equation y = k/x?
A.
Linear functions
B.
Hyperbolas
C.
Parabolas
D.
Circles
Show solution
Solution
The equation y = k/x represents a family of hyperbolas with varying asymptotes depending on the value of 'k'.
Correct Answer: B — Hyperbolas
Learn More →
Q. What is the general form of the family of curves for the equation x^2 + y^2 = r^2?
A.
Ellipses
B.
Hyperbolas
C.
Circles
D.
Parabolas
Show solution
Solution
The equation x^2 + y^2 = r^2 represents a family of circles with varying radii (r).
Correct Answer: C — Circles
Learn More →
Q. What is the general form of the family of curves represented by the equation x^2 + y^2 = r^2?
A.
Circles with radius r
B.
Ellipses with semi-major axis r
C.
Hyperbolas with transverse axis r
D.
Straight lines with slope r
Show solution
Solution
The equation x^2 + y^2 = r^2 represents a family of circles with radius r centered at the origin.
Correct Answer: A — Circles with radius r
Learn More →
Q. What is the general form of the family of curves represented by the equation y = mx^2 + c?
A.
Parabolas
B.
Circles
C.
Ellipses
D.
Hyperbolas
Show solution
Solution
The equation y = mx^2 + c represents a family of parabolas that open upwards or downwards depending on the sign of m.
Correct Answer: A — Parabolas
Learn More →
Q. What is the general form of the family of curves represented by y^2 = 4ax?
A.
Parabolas opening to the right
B.
Circles with varying centers
C.
Ellipses with varying foci
D.
Hyperbolas with varying asymptotes
Show solution
Solution
The equation y^2 = 4ax represents a family of parabolas that open to the right with varying values of 'a'.
Correct Answer: A — Parabolas opening to the right
Learn More →
Q. What is the length of the diagonal of a rectangle with vertices at (0, 0), (0, 4), (3, 0), and (3, 4)?
Show solution
Solution
Diagonal length = √[(3-0)² + (4-0)²] = √[9 + 16] = √25 = 5.
Correct Answer: C — 5
Learn More →
Q. What is the length of the diameter of a circle with radius 7?
Show solution
Solution
The diameter is twice the radius, so 2 * 7 = 14.
Correct Answer: B — 14
Learn More →
Q. What is the length of the diameter of a circle with the equation (x - 1)² + (y + 2)² = 16?
Show solution
Solution
The radius is √16 = 4, so the diameter is 2 * radius = 8.
Correct Answer: B — 8
Learn More →
Q. What is the length of the latus rectum of the ellipse x^2/36 + y^2/16 = 1?
A.
8/3
B.
12
C.
16/3
D.
24
Show solution
Solution
The length of the latus rectum is given by (2b^2/a). Here, b^2 = 16, a^2 = 36, so length = (2*16/6) = 12.
Correct Answer: B — 12
Learn More →
Q. What is the length of the latus rectum of the ellipse x^2/a^2 + y^2/b^2 = 1?
A.
2b^2/a
B.
2a^2/b
C.
2a
D.
2b
Show solution
Solution
The length of the latus rectum of the ellipse is given by 2a^2/b.
Correct Answer: B — 2a^2/b
Learn More →
Q. What is the length of the latus rectum of the parabola y^2 = 12x?
Show solution
Solution
The length of the latus rectum of a parabola given by the equation y^2 = 4px is 4p. Here, 4p = 12, so p = 3. Therefore, the length of the latus rectum is 4p = 12.
Correct Answer: B — 6
Learn More →
Q. What is the length of the latus rectum of the parabola y^2 = 4ax?
A.
2a
B.
4a
C.
a
D.
None of the above
Show solution
Solution
The length of the latus rectum of the parabola y^2 = 4ax is 4a.
Correct Answer: A — 2a
Learn More →
Q. What is the length of the latus rectum of the parabola y^2 = 8x?
Show solution
Solution
The length of the latus rectum of the parabola y^2 = 8x is 4.
Correct Answer: A — 4
Learn More →
Q. What is the length of the line segment joining the points (-1, -1) and (2, 3)?
Show solution
Solution
Length = √[(2 - (-1))² + (3 - (-1))²] = √[3² + 4²] = √25 = 5.
Correct Answer: C — 5
Learn More →
Q. What is the length of the line segment joining the points (1, 2) and (1, 5)?
Show solution
Solution
Length = |5 - 2| = 3.
Correct Answer: A — 3
Learn More →
Q. What is the length of the segment of the line 3x + 4y = 12 between the x-axis and y-axis?
Show solution
Solution
The x-intercept is (4, 0) and the y-intercept is (0, 3). The length of the segment is sqrt((4-0)^2 + (0-3)^2) = sqrt(16 + 9) = 5.
Correct Answer: B — 6
Learn More →
Q. What is the midpoint of the line segment joining the points (1, 2) and (3, 4)?
A.
(2, 3)
B.
(1, 2)
C.
(3, 4)
D.
(4, 6)
Show solution
Solution
Midpoint = ((1+3)/2, (2+4)/2) = (2, 3).
Correct Answer: A — (2, 3)
Learn More →
Q. What is the midpoint of the line segment joining the points (2, 3) and (4, 7)?
A.
(3, 5)
B.
(2, 5)
C.
(4, 3)
D.
(5, 7)
Show solution
Solution
Midpoint = ((2+4)/2, (3+7)/2) = (3, 5).
Correct Answer: A — (3, 5)
Learn More →
Q. What is the radius of the circle given by the equation (x - 1)² + (y + 4)² = 16?
Show solution
Solution
The radius is the square root of 16, which is 4.
Correct Answer: A — 4
Learn More →
Q. What is the slope of the line passing through the points (1, 2) and (3, 6)?
Show solution
Solution
Slope = (6-2)/(3-1) = 4/2 = 2.
Correct Answer: A — 2
Learn More →
Q. What is the slope of the line passing through the points (2, 3) and (4, 7)?
Show solution
Solution
Slope = (7-3)/(4-2) = 4/2 = 2.
Correct Answer: A — 2
Learn More →
Q. What is the slope of the line perpendicular to the line y = -2x + 3?
A.
-1/2
B.
1/2
C.
2
D.
-2
Show solution
Solution
The slope of the given line is -2. The slope of the perpendicular line is the negative reciprocal, which is 1/2.
Correct Answer: B — 1/2
Learn More →
Q. What is the slope of the line perpendicular to the line y = -2x + 4?
A.
0.5
B.
2
C.
-0.5
D.
-2
Show solution
Solution
The slope of the given line is -2. The slope of the perpendicular line is the negative reciprocal, which is 1/2.
Correct Answer: B — 2
Learn More →
Q. What is the slope of the line perpendicular to the line y = -3x + 4?
A.
1/3
B.
-1/3
C.
3
D.
-3
Show solution
Solution
The slope of the given line is -3. The slope of the perpendicular line is the negative reciprocal: 1/3.
Correct Answer: C — 3
Learn More →
Q. What is the slope of the line represented by the equation 2x - 3y + 6 = 0?
A.
2/3
B.
3/2
C.
-2/3
D.
-3/2
Show solution
Solution
Rearranging gives y = (2/3)x + 2, slope = 2/3.
Correct Answer: C — -2/3
Learn More →
Q. What is the slope of the line represented by the equation 3x - 4y + 12 = 0?
A.
3/4
B.
4/3
C.
-3/4
D.
-4/3
Show solution
Solution
Rearranging gives y = (3/4)x + 3. Slope = 3/4.
Correct Answer: C — -3/4
Learn More →
Q. What is the slope of the line represented by the equation 5y - 10x = 20?
Show solution
Solution
Rearranging to slope-intercept form: 5y = 10x + 20 => y = 2x + 4. The slope is 2.
Correct Answer: C — 0.5
Learn More →
Q. What is the slope of the line that passes through the points (0, 0) and (4, 8)?
Show solution
Solution
The slope m = (8 - 0) / (4 - 0) = 2.
Correct Answer: C — 2
Learn More →
Q. What is the slope of the lines represented by the equation 5x^2 - 10xy + 5y^2 = 0?
Show solution
Solution
The equation can be factored to find the slopes, which are both 1.
Correct Answer: A — 1
Learn More →
Q. What is the slope of the lines represented by the equation x^2 - 6xy + 9y^2 = 0?
Show solution
Solution
Factoring gives (x - 3y)^2 = 0, indicating a double root, hence the slope is 3.
Correct Answer: A — 3
Learn More →
Showing 301 to 330 of 361 (13 Pages)
