Class 12 Mathematics Chapter 6 – Analytical Geometry MCQs| FBISE | Grade 12 Math
Practice 50 exam-oriented Class 12 Mathematics Chapter 6 Analytical Geometry MCQs for FBISE HSSC-II. These questions cover coordinate geometry, straight lines, circles, parabola, ellipse, hyperbola, eccentricity, tangents and related applications.
1. The coordinates of a point in the Cartesian plane are written as
A) (x,y) B) [x,y] C) (x+y) D) [x-y]
2. The point where the coordinate axes intersect is called the
A) focus B) origin C) vertex D) midpoint
3. The distance between (x₁,y₁) and (x₂,y₂) is
A) 1 B) 0 C) √((x₂−x₁)²+(y₂−y₁)²) D) −1
4. The midpoint of two points (x₁,y₁) and (x₂,y₂) is
A) −1 B) 0 C) 1 D) ((x₁+x₂)/2,(y₁+y₂)/2)
5. The slope of a line through two points is
A) (y₂−y₁)/(x₂−x₁) B) 0 C) 1 D) −1
6. A horizontal line has slope
A) 1 B) 0 C) undefined D) −1
7. A vertical line has slope
A) 0 B) 1 C) undefined D) −1
8. The slope of y=3x+2 is
A) 2 B) 1/3 C) −2 D) 3
9. The point-slope equation of a line is
A) y−y₁=m(x−x₁) B) y+y₁=m(x+x₁) C) x−x₁=m(y−y₁) D) y=mx+y₁x₁
10. The slope-intercept form of a straight line is
A) x=my+c B) y=mx+c C) xy=mc D) y=m/x+c
11. The slope of 2x+3y=6 is
A) 2/3 B) 3/2 C) −2/3 D) −3/2
12. Two non-vertical lines are parallel when their slopes are
A) opposite B) negative reciprocals C) zero D) equal
13. Two non-vertical lines are perpendicular when the product of their slopes is
A) −1 B) 1 C) 0 D) 2
14. The angle θ between lines of slopes m₁,m₂ satisfies
A) tanθ=(m₁+m₂)/(1−m₁m₂) B) tanθ=|(m₂−m₁)/(1+m₁m₂)| C) tanθ=m₁m₂ D) tanθ=m₁−m₂
15. The equation of the x-axis is
A) x=0 B) x=y C) y=0 D) y=1
16. The equation of the y-axis is
A) y=x B) y=0 C) x=1 D) x=0
17. The distance of (3,4) from the origin is
A) 5 B) 4 C) 3 D) 7
18. The midpoint of (2,4) and (6,8) is
A) (2,2) B) (4,6) C) (8,12) D) (3,4)
19. The slope through (1,2) and (3,6) is
A) 1 B) 3 C) 2 D) 4
20. The line through (0,2) with slope 3 is
A) y=2x+3 B) y=x+2 C) y=3x−2 D) y=3x+2
21. The equation of a circle with centre (h,k) and radius r is
A) (x−h)²+(y−k)²=r² B) (x+h)²+(y+k)²=r C) (x−h)+(y−k)=r² D) x²+y²=r
22. The centre of x²+y²=25 is
A) (5,0) B) (0,0) C) (0,5) D) (−5,0)
23. The radius of x²+y²=49 is
A) 49 B) 14 C) 7 D) √7
24. The centre of (x−2)²+(y+3)²=16 is
A) (−2,3) B) (−2,−3) C) (2,3) D) (2,−3)
25. The radius of (x−2)²+(y+3)²=16 is
A) 4 B) 3 C) 2 D) 16
26. The general equation of a circle is
A) x²−y²+2gx=0 B) x²+y²+2gx+2fy+c=0 C) x²+y²+gx+fy=1 D) x+y+c=0
27. The centre of x²+y²+2gx+2fy+c=0 is
A) (g,f) B) (2g,2f) C) (−g,−f) D) (−2g,−2f)
28. Its radius is
A) √(c−g−f) B) √(g²+f²+c) C) g²+f²−c D) √(g²+f²−c)
29. A parabola with vertex at origin opening along +x has equation
A) y²=4ax B) x²=4ay C) y=4ax² D) x²=4a
30. For y²=4ax, the focus is
A) (0,a) B) (a,0) C) (−a,0) D) (0,−a)
31. For y²=4ax, the directrix is
A) x=a B) y=a C) x=−a D) y=−a
32. For y²=4ax, the length of latus rectum is
A) a B) 2a C) 8a D) 4a
33. The parabola x²=4ay opens
A) upward B) left C) right D) downward
34. For x²=4ay, the focus is
A) (a,0) B) (0,a) C) (−a,0) D) (0,−a)
35. The standard ellipse with major axis on x-axis is
A) x²−y²=1 B) x²/a+y²/b=0 C) x²/a²+y²/b²=1, a>b D) y²=4ax
36. For an ellipse, the relation among a,b,c is
A) a=b+c B) c²=a²+b² C) b²=a²+c² D) a²=b²+c²
37. The eccentricity of an ellipse is
A) c/a B) a/c C) b/c D) c/b
38. The eccentricity of an ellipse is
A) greater than 1 B) less than 1 C) equal to 1 D) always zero
39. The standard hyperbola with transverse axis on x-axis is
A) y²=4ax B) x²/a²+y²/b²=1 C) x²/a²−y²/b²=1 D) x²+y²=a²
40. For x²/a²−y²/b²=1, the relation is
A) c²=a²−b² B) a²=b²+c² C) b²=a²+c² D) c²=a²+b²
41. The eccentricity of a hyperbola is
A) greater than 1 B) equal to 1 C) less than 1 D) always zero
42. The asymptotes of x²/a²−y²/b²=1 are
A) y=±ax/b B) y=±bx/a C) x=±a D) y=±a
43. A conic with eccentricity e=1 is a
A) circle B) ellipse C) parabola D) hyperbola
44. A conic with eccentricity e<1 is an
A) straight line B) parabola C) hyperbola D) ellipse
45. A conic with eccentricity e>1 is a
A) hyperbola B) ellipse C) parabola D) circle
46. x²+y²+2x−4y−4=0 represents a
A) parabola B) circle C) hyperbola D) straight line
47. Completing the square is useful for finding the
A) time of motion B) slope of every line C) centre and radius of a circle D) derivative
48. The radius drawn to the point of contact of a tangent to a circle is
A) parallel to tangent B) twice tangent C) equal to tangent D) perpendicular to tangent
49. A chord is a line segment whose endpoints lie
A) on the circle B) at the centre C) outside the circle D) on the tangent
50. The perpendicular from the centre of a circle to a chord
A) doubles the chord B) bisects the chord C) is tangent to every chord D) has zero length
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This set covers the Class 12 Mathematics Analytical Geometry content represented in the uploaded chapter file, with the MCQs and chapter terminology preserved from the source.
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