ECAT Mathematics Chapter 20 Analytic Geometry Online Test

The point which divides the line joining the points (2, 4, 5) and (3, 5, -4) in the ratio -2 : 3 lines on

• ZOX plane A
• XOY plane B
• YOZ plane C
• None of these D

If the lines 2x-3y-1=0,3x-y-5=0 and 3x+py+8=0 meet at a unique point then

• p = -14 A
• p = -1 B
• p =0 C
• p=12 D

The straight lines represented by the equation ax2+ 2hxy +by2 =0 intersects at

• (1,1) A
• (0,1) B
• (1,0) C
• (0,0) D

The points A(3,1),B(-2,-3),C(2,2) are vertices of an (an)

• Right triangle A
• Equilateral triangle B
• Isosceles triangle C
• Scalene triangle D

If distance of (a,b) from origin is 5 then

• a²+ b²=5 A
• a = 5 B
• b = 5 C
• 
  D

The mid point of the line segment joining the points (3,-1) and (-3,1) is

• (3,-1) A
• (0,0) B
• (2,2) C
• (4,4) D

The distance of the point (-2,3) from x-axis is

• -2 A
• 2 B
• 3 C
• 1 D

The distance between the points A(-8,3) and B(2,-1) is

• 
  A
• 116 B
• 
  C
• none of these D

• 
  A
• 
  B
• 
  C
• 
  D

The point R dividing externally the line joining the points P(x₁, y₁) and Q(x₂, y₂) in the ratio k₁: k₂has the coordinates

• 
  A
• 
  B
• 
  C
• 
  D

The distance between the points A(3,1) and B(-2,-4) is

• 5 A
• 
  B
• 25 C
• 10 D

• 0 A
• 1 B
• -1 C
• undefined D

• 
  A
• 
  B
• 
  C
• 
  D

If origin is the mid point of (a, -3) and (-5, b) then

• a = -5 , b = -3 A
• a = 5 , b =3 B
• a = -5 , b = 3 C
• a = 5 , b = -3 D

For all points (x,y) on y-axis

• x is positive A
• x = 0 B
• x is negative C
• y = 0 D

If distance between (3,b) and (0,0) is 3 then b = _______

• 3 A
• 
  B
• 9 C
• 0 D

If A(x₁, y₁) , B(x₂, y₂) and C(x₃, y₃) are the vertices of a triangle then its centroid is

• 
  A
• 
  B
• 
  C
• 
  D

If line through (4,3) and (2,k) is perpendicular to y =2x +3, then k =_______

• -1 A
• 1 B
• -4 C
• 4 D

• 
  A
• 
  B
• 
  C
• 
  D

• Parallel to the plane A
• At right angles to the plane B
• Lies in the plane C
• Meet the plane obliquely D

The distance between the points (1, 2) and (2, 1) is

• 3 A
• 6 B
• 
  C
• 
  D

The direction cosines of any normal to the xy-plane are

• <1, 0, 0> A
• <0, 1, 0> B
• <1, 1, 0> C
• <0, 0, 1> D

The distance of the point (-2 , 3) from y-axis is

• 2 A
• -2 B
• 3 C
• 1 D

• 3 A
• 1 B
• 4 C
• 
  D

The slope of x-axis is

• 0 A
• undefined B
• 1 C
• 
  D

The intercepts of the plane 2x - 3y + 4z = 12 on the co-ordinate axes are given by

• 2, -3, 4 A
• 6, -4, -3 B
• 6, -4, 3 C
• 3, -2, 1.5 D

The inclination of a line parallel to y-axis is

• 
  A
• 
  B
• 
  C
• 
  D

For all points (x,y) in fourth quadrant

• x > 0 , y < 0 A
• x > 0 , y > 0 B
• x < 0 , y < 0 C
• x < 0 , y > 0 D

The point of concurrency of the angle bisectors of a triangle is called

• incentre A
• circumcentre B
• e-centre C
• centroid D

The distance of the point (-2, -3) from the origin is

• 2 A
• -5 B
• -3 C
• 
  D