68 free MCQs on Straight Lines, each with its own worked answer and explanation. Points, lines, and curves on the Cartesian plane
Take the timed Straight Lines chapterwise test →68 practice questions on Straight Lines, sorted Easy → Hard. Try each one first, then open its answer page for the worked explanation. Want the full theory first? Read the Straight Lines notes.
The slope of a line is the ratio of vertical change (rise) to horizontal change (run) between any two points on it - equivalently, the tangent of the angle θ the line makes with the positive x-axis.
Q8.
The slope-intercept form of a line is:
Q11.
The centroid of triangle with vertices (0,0), (6,0), (0,6) is:
Q12.
Two parallel lines have:
Q13.
Two perpendicular lines have slopes m<sub>1</sub> and m<sub>2</sub> where:
Q16.
Which of these points is on the line y = 2x + 1?
Q17.
The standard form of a circle centred at origin with radius r is:
Q18.
The point dividing (2,3) and (8,9) internally in ratio 1:2 is:
Q19.
Area of triangle with vertices (0,0), (4,0), (0,3) is:
Q20.
The equation y = c (constant) represents:
Q21.
The equation of a line through (1,2) parallel to 3x + 4y = 5 is:
Q22.
The distance from point (3,-4) to line 3x - 4y + 5 = 0 is:
Q23.
Find the area of triangle with vertices (0,0), (3,0), (0,4).
Q24.
The centre of circle x² + y² - 6x + 8y + 5 = 0 is:
Q26.
Three points (1,1), (2,3), (3,5) are:
Q27.
The equation of the perpendicular from origin to the line x + y = 5 is:
Q28.
Find the equation of line with x-intercept 3 and y-intercept 4.
Q30.
The locus of points equidistant from (3,0) and (-3,0) is:
Q32.
Equation of tangent to circle x² + y² = 25 at point (3,4) is:
Q34.
The point (2,3) divides line segment from (0,0) to (6,9) in ratio:
Q35.
The foot of perpendicular from (3,4) to x-axis is:
Q36.
Equation of line through origin and (3,5) is:
Q37.
The vertex of parabola y = (x-2)² + 3 is:
Q38.
The image of (3,5) in the line y = x is:
Q39.
Two lines 3x + 2y = 7 and 6x + 4y = 10 are:
Q40.
The combined equation of x-axis and y-axis is:
Q41.
The pair of lines 2x² + 5xy + 2y² = 0 represents:
Q42.
The equation of director circle of ellipse x²/a² + y²/b² = 1 is:
Q43.
The asymptotes of hyperbola x²/a² - y²/b² = 1 are:
Q45.
If the line x/a + y/b = 1 passes through the intersection of 2x+3y=5 and x-2y=1 and is parallel to y=x, find a+b.
Q46.
The chord of contact of tangents from (h,k) to circle x²+y²=r² is:
Q47.
Equation of normal to parabola y² = 4ax at point (at², 2at) is:
Q48.
Three circles pass through the origin. The radical axis of any two of them:
Q49.
The combined equation of lines joining origin to intersection of y = mx + c and x² + y² = a² is:
Q50.
If a point moves such that its distances from (3,0) and (-3,0) sum to 10, it traces:
Q51.
The equation of tangent to ellipse x²/a² + y²/b² = 1 with slope m is:
Q52.
The angle between two circles intersecting orthogonally satisfies:
Q53.
Centres of two circles are (0,0) and (5,0). Radii are 3 and 2. Circles are:
Q54.
The locus of midpoints of parallel chords of a parabola is:
Q55.
Area of triangle formed by lines y = 0, x = 0, and lx + my = 1 is:
Q56.
The condition for three points (x₁,y₁), (x₂,y₂), (x₃,y₃) to be collinear is:
Q58.
The slope of a line perpendicular to y = 2x + 3 is:
Q59.
The equation of a line with slope 2 passing through (0, 3) is:
Q60.
The distance of the point (1, 1) from the line 3x + 4y − 12 = 0 is:
Q61.
The foot of the perpendicular from (1, 2) to the line 3x + 4y − 5 = 0 is:
Q62.
The area of the triangle formed by the lines y = x, y = −x and y = 2 is:
Q63.
The image of the point (3, 8) in the line x + 3y = 7 is:
Q64.
The distance between the parallel lines 3x + 4y = 9 and 3x + 4y = 1 is:
Q65.
The acute angle between the lines y = √3 x and y = x/√3 is:
Q66.
The equation of the line through (2, 3) perpendicular to 3x − 4y + 5 = 0 is:
Q67.
The value of k for which 3x + ky = 1 passes through the intersection of x + 2y = 3 and 2x + y = 3 is:
Q68.
The orthocentre of the triangle with vertices (0, 0), (4, 0) and (0, 6) is:
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