Introduction to LOCI

Q.

The locus of a point equidistant from two parallel lines is

1. any line parallel to both the lines

2. a line parallel to both the lines and midway between them

3. the perpendicular bisector of any one of the parallel lines

4. any line perpendicular to both the lines

Q.

AB is a fixed line. State the locus of the point P so that AB${}^2$= AP${}^2$+ BP${}^2$

1. Circle with diameter AB

2. Circle with diameter 3AB

3. None of these

4. Circle with radius AB

Q.

A and B are two fixed points. What will be the locus of the point P such that $\angle APB={90}^{\circ }$

1. The locus of point P is the perpendicular bisector of line joining AB.

2. The locus of point P is the circumference of a circle with AB as the diameter.

3. The locus of point P is the circumference of a semi-circle with AB as the diameter.

4. The locus of P is any circle passing through the points A and B.

Q.

What is the locus of the centre of a cycle wheel?

1. Curved path

2. Concentric circle

3. Line diagonal to the ground

4. Straight line parallel to the ground

Q. What is meant by the locus of points?

1. A set of points which satisfies some given conditions.

2. A set of random points.

3. None of these

4. A line joining two points.

Q.

The locus of a point which is equidistant from two given parallel lines is a line ___ to the given lines and it is the midway between them.

1. parallel

2. intersecting at 60 degrees

3. intersecting at 30 degrees

4. perpendicular

Q.

The locus of the point which moves in such a way that its distance from the line $x=6$ is always equal to 2 units is

1. the line $x=4$.

2. the line $x=8$.

3. lines $x=4$ and $x=8$.

4. y-axis.

Q.

The locus of the point which moves in such a way that its distance from the line $y=-6$ is always equal to 1 unit is

1. the line y=-4

2. the line y=6

3. the line y=-5 and the line y=-7

4. $x$ - axis

Q.

The locus of mid-points of all parallel chords in a circle is

1. the diameter of the circle which is perpendicular to the given chords

2. any chord of the circle

3. any diameter of the circle

4. any chord of the circle which is perpendicular to the given chords

Q.

The locus of a point P with $\angle APB$ as ${90}^{\circ }$ will be a circle if AB is the diameter.

1. True

2. False