Coordinate Geometry
Q. What is the equation of the line that passes through the origin and has a slope of -3? (2022)
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A.
y = -3x
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B.
y = 3x
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C.
y = -x/3
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D.
y = 1/3x
Solution
The equation of a line through the origin with slope m is y = mx. Thus, y = -3x.
Correct Answer: A — y = -3x
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Q. What is the equation of the line that passes through the origin and has a slope of -4? (2023)
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A.
y = -4x
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B.
y = 4x
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C.
y = -x/4
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D.
y = 1/4x
Solution
Using the slope-intercept form y = mx + b, with m = -4 and b = 0, the equation is y = -4x.
Correct Answer: A — y = -4x
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Q. What is the latus rectum of the parabola given by the equation y^2 = 12x?
Solution
The latus rectum of a parabola y^2 = 4px is given by 4p. Here, 4p = 12, so p = 3, and the latus rectum is 4p = 12.
Correct Answer: C — 6
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Q. What is the value of p for the parabola defined by the equation y^2 = 20x?
Solution
In the equation y^2 = 4px, we have 4p = 20, thus p = 5.
Correct Answer: A — 5
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Q. What is the y-intercept of the line given by the equation 5x - 2y = 10? (2023)
Solution
Rearranging to slope-intercept form: -2y = -5x + 10, thus y = (5/2)x - 5. The y-intercept is -5.
Correct Answer: D — -2
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Q. Which of the following points lies on the parabola y = x^2 - 4?
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A.
(2, 0)
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B.
(0, -4)
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C.
(1, -3)
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D.
(3, 5)
Solution
Substituting x = 1 into the equation gives y = 1^2 - 4 = -3, so the point (1, -3) lies on the parabola.
Correct Answer: C — (1, -3)
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