Mathematics ECAT Pre Engineering Chapter 18 Analytic Geometry Online Test

The distance of the point (a,b) from y-axis is

• a A
• b B
• a + b C
• 
  D

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

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

The equation of the sphere passing thro' (0, 0, 0), (a, 0, 0), (0, b, 0), (9, 0, c) is

• x²+ y²+ z²+ 2 ax +2 by + 2cz = 0 A
• x²+ y²+ z²- 2ax - 2 by - 2cz = 0 B
• x²+ y²+ z²- ax - by - cz = 0 C
• x²+ y²+ z²+ ax + by + cz = 0 D

The equation of the sphere thro' the origin and making intercepts a, b, c on co-ordinate axes is

• x²+ y²+ z²+ ax + by + cz = 0 A
• x²+ y²+ z²- 2ax - 2 by - 2 cz = 0 B
• x²+ y²+ z²= a + b + c C
• x²+ y²+ z² - ax - by - cz =0 D

If d₁is the distance between (0,0) and (1,2) and d₂is the distance between (0,0) and (-1,-2) the

• d₁< d₂ A
• d₁> d₂ B
• d₁= d₂ C
• none of these D

The centroid of a triangle divides each median in the ratio

• 2 : 1 A
• 3 : 1 B
• 3 : 2 C
• 1 : 1 D

(-28,12) divides the join of A(-6,3) and B(5,-2) in ratio

• 1:2 A
• 3:2 B
• 2:3 C
• 2:1 D

The distance between two points P(x₁, y₁) and Q (x₂, y₂) is

• 
  A
• 
  B
• 
  C
• 
  D

Number of lines passing through three non-collinear points is

• 2 A
• 3 B
• 1 C
• 0 D
• ∞ E

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

The mid point of the line segment joining the points (4,0) and (0,4) is

• (4,4) A
• (2,2) B
• (-4,-4) C
• (-2,-2) D

The distance of the point (1.1) from the origin is

• 0 A
• 2 B
• 
  C
• 
  D

The coordinates of a point P(x,y) referred to XY-system are

• (x+y,y+k) A
• (x-h,y-k) B
• (x,y) C
• (x-h,y-k) D

If (2, 3) is the mid point of (a, 3) and (5, b) then

• a = 1 , b = -3 A
• a = -1 , b = 3 B
• a = 1 , b =3 C
• a = -1 , b = -3 D

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

• 2 A
• 3 B
• 5 C
• 
  D

• 0 A
• 
  B
• 
  C
• undefined D

A quadrilateral whose diagonals are perpendicular bisector of each other is

• Square A
• Rectangle B
• Rhombus C
• Parallelogram D
• Trapezium E

64.A point (x, y, z) moves parallel to xy plane. Which of the three variables x, y, z remain fixed?

• z A
• x B
• y C
• x and y D

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

• 2 A
• -2 B
• 3 C
• -3 D

• 
  A
• 
  B
• 
  C
• 
  D

• 1 A
• 2 B
• -1 C
• 0 D

If k2x2 +2hxy- 4y2 =0 represents two perpendicular lines then

• k = 2 A
• k = ±2 B
• k = -2 C
• k ≠0 D

A joint equation of the lines through the origin and perpendicular to the lines ax2 +2hxy +by2 =0 is indentical is ax2 +2hxy +by2 =0 if

• h2 = ab A
• a + b =0 B
• a = b C
• a≠ b D
• a = b = 0 E

If l, m, n are the d.c.'s of a line, then

• l2+ m2+ n2= 0 A
• l2+ m2+ n2= 1 B
• l + m + n = 1 C
• l = m = n = 1 D

For all points (x,y) in first quadrant

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

The coordinates of the point that divides the join of A(-6,3) and B(5, -2) in the ratio 2:3 internally

• 
  A
• 
  B
• 
  C
• 
  D

The mid point of the line segment joining the points (a,b) and (b,a) is

• 
  A
• 
  B
• 
  C
• 
  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 st. lines whose direction cosines satisfy al + bm + cn = 0, fmn + gnl + hlm=0 are perpendicular if

• 
  A
• 
  B
• 
  C
• 
  D

If the points (a,2b):(c,a+b):(2c-a,h) lie on the same line then

• h=2a A
• h=a+b B
• h=ab C
• h=ac D