Coordinates of a Point in Space

Q.

The coordinates of the focus and length of latus-rectum of the parabola y² = 8x is:

1. (2, 0), 16

2. (4, 0), 16

3. (4, 0), 8

4. (2, 0), 8

Q.

The new coordinates of a point (4, 5), when the origin is shifted to the point (1, -2) are

1. (5, 3)

2. (3, 5)

3. (3, 7)

4. None of these

Q. Find the coordinates of the point where the line joining A(3, 4, 1) and B(5, 1, 6) crosses the xy-plane.

Q.

A point is on the XZ-plane. What can you say about its y-coordinate?

Q.

The coordinate planes divide the space into ___ octants.

Q. Three vertices of a parallelogram ABCD are A(3, -1, 2), B(1, 2, -4) and C(-1, 1, 2). Find the coordinates of the fourth vertex D.

Q.

Name the octants in which the following points lie (1, 2, 3), (4, -2, 3), (4, -2, -5), (-4, 2, -5), (-4, 2, 5), (-4, 2, 5), (-3, -1, 6), (2, -4, -7)

Q.

Find the ratio in which the line segment joining the points (4, 8, 10) and (6, 10, -8) is divided by the YZ-plane.

1. internally in the ratio 2:3

2. externally in the ratio 2:3

3. internally in the ratio 1:2

4. externally in the ratio 1:2

Q.

Find the equation of the set of points P, the sum of whose distance from $A(4,0,0)$ and $B(-4,0,0)$ is equal to 10.

Q. Determine the point in xy-plane which is equidistant from three points A(2, 0, 3), B(0, 3, 2) and C(0, 0, 1).

Q.

Find the ratio in which the line segment joining points (2, -1, 3) and (-1, 2, 1) is divided by the plane x + y + z = 5.

Q.

Find the equation of the curve formed by the set of all points whose distances from the points (3, 4, -5) and (-2, 1, 4) are equal.

Q.

A point is on the x-axis. What are its y-coordinates and z-coordinates?

Q.

The equation of circle of radius 5 units touches the coordinates axes in the second quadrant is:

1. x² + y² + 10x + 10y + 25 = 0

2. x² + y² – 10x – 10y – 25 = 0

3. x² + y² + 10x – 10y + 25 = 0

4. x² + y² – 10x – 10y + 25 = 0

Q.

The image of (–2, 3, 4) in the yz -plane is:

1. (0, 3, 4)

2. (– 2, 0, 0)

3. (2, 0, 0)

4. (2, 3, 4)

Q.

If $z_1,z_2,z_{3}and{z}_4$ be the consecutive vertices of a square, then $z_1^2+z_2^2+z_3^2+z_4^2$ equals

1. 

2. 

3. 0

4. None of the above

Q. Find the coordinates of the midpoint of the line segment joining the points A(-2, -5) and B(3, -1).

Q.

If origin is shifted to the point (h, k) the new coordinate of (x, y) will be (x+h, y+k)

1. True

2. False

Q.

Find the distance between the points $A(-2,1,-3)$ and $B(4,3,-6)$.

Q.

The equation of the set of points which are equidistant from (1, 2, 3) and (3, 2, -1).

1. x = 2z

2. x+2y+3z=0

3. x+2z=0

4. 2y-3z=0

Q.

At what point the origin be shifted, if the coordinates of a point (6, 7) becomes (-1, 11) ?

1. (-7, 4)

2. (4, -7)

3. (7, -4)

4. (7, 4)

Q.

If A and B be the points $(3,4,5)$ and $(-1,3,-7)$ respectively, find the equation of the set of points P such that $P{A}^2+P{B}^2=k^2$ where k is a constant.

Q.

A point moves so that its distance from the point (-1, 0) is always three times its distance from the point (0, 2). The locus of the point is

1. A line

2. A circle

3. A parabola

4. An ellipse

Q.

Find the point to which the origin be shifted after a translation, so that the equation $x^2+y^2-4x-8y+3=0$will have no first degree terms.

Q.

The region representing the solution of the system of inequalities 4x + 5y ≤ 20, 5x + 2y ≤ 20, x ≥ 0, is a

1. Quadrilateral

2. Unbounded region

3. Pentagon

4. Triangle

Q. The point lies on XZ plane.

1. (1, 2, 3)
2. (1, 0, 1)
3. (1, 1, 0)
4. (0, 2, 3)

Q.

The distances of the point (1, 2, 3) from the coordinate axes are A, B and C respectively. Which option is correct?

1. 2A²C² = 13B²

2. A² = B² + C²

3. B² = 3C²

4. A² = 2C²

Q.

The locus of a point which moves so that its distance from x-axis is double of its distance from y-axis is

1. 

2. 

3. 

4. 

Q.

Which of the following points lie in the VII th octant?

1. (1, 2, -8)

2. (2, -1, -2)

3. (-2, -3, -10)

4. (-5, 0, -4)

Q.

Which of the following points lie on the x-y plane?

1. (1, 5, 0)

2. (0, 0, -6)

3. (7, 0, 6)

4. (0, 2, -5)