Introduction to LOCI

Q. 35. Two circular flower beds have been shown on two sides of a square lawn ABCD of side 56m. If the centre of each circular flower bed is the point of intersection O of the diagonals of square lawn, find the sum of the lawn and flower beds.

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. Question 8
If one of the angles formed by two intersecting lines is a right angle, what can you say about the other three angles? Give the reason for your answer.

Q. The locus of points, equidistant from two intersecting lines form the between the lines.

1. angle bisector
2. area
3. angle

Q.

What are you doing there? Here ‘there’ is a or an?

1. verb

2. adjective

3. adverb

4. noun

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.

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.

Construct $\Delta$PQR with QR = 6.5 cm, PQ= 5.5 cm, PR = 5 cm. Construct and find the radius of incircle of the $\Delta$PQR

1. 3.2 cm

2. 2.8 cm

3. 4.6 cm

4. 1.6 cm

Q.

The locus of a point equidistant from two parallel lines is a line parallel to both the lines. State whether true or false.

1. True

2. False

Q. Construct a triangle ABC in which BC = 6.3 cm, $\angle B={120}^{\circ }$ and BA = 4.6 cm. Draw its circumcircle. [3 MARKS]

Q.

The locus of $Z$ satisfying the inequality $\left|\frac{z+2i}{2z+i}\right|<1$, where $Z=x+iy$ is

1. $x^2+y^2<1$

2. $x^2-y^2<1$

3. $x^2+y^2>1$

4. $2x^2+3y^2<1$

Q. Construct a triangle ABC with AB = 5.5 cm, AC = 6 cm and $\angle BAC={105}^{\circ }$. Mark the point of intersection of the locus of points equidistant from BA and BC and the locus of points equidistant from B and C, as P. Then the length of PC is ___ cm.

1. 4.8

Q. If two circle intersect at two points , prove that their centres lie on the perpendicular bisector of common chord.

Q. Let a, b, x and y be real numbers such that a-b=1 and $y\ne 0$. If the complex number z=x+iy satisfies Im $\frac{(az+b)}{(z+1)}=y$, then which of the following is (are) possible value(s) of x?

1. ($1-\sqrt{1+y^2}$) & ($-1-\sqrt{1+y^2}$)
2. ($-1-\sqrt{1-y^2}$) & ($-1+\sqrt{1-y^2}$)
3. ($1+\sqrt{1+y^2}$) & ($1-\sqrt{1+y^2}$)
4. ($-1-\sqrt{1+y^2}$) & ( $-1-\sqrt{1-y^2}$)

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.

Which function models the graph below?

X –axis 1 grid = 1 unit

Y –axis 1 grid = 1 unit

1. y =(x + 2)²+ 4

2. y = (x - 4)²+ 2

3. y = (x + 4)²+ 2

4. y =(x - 4)² - 2

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

Q. What is locus ?

Q.

The locus of points within a circle that is equidistant from the endpoints of a given chord is a diameter which is perpendicular bisector of the given chord.

1. False

2. True

Q.

Construct a $\Delta$PQR with QR = 8, PQ= 6 PR = 4. Construct the incircle of the triangle and find the radius of the incircle.

1. 4.2 cm

2. 5.4 cm

3. 4 cm

4. 2.2 cm

Q.

Chords AB & CD (not the diameters) of a circle intersect at point P inside the circle.

Find the sum of the angles subtended at the centre of the circle by the arcs AC & BD in terms of ∠APC.

1. ∠APC

2. 1.5∠APC

3. 1.2∠APC

4. 1.8∠APC

5. 2∠APC

Q.

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

1. Circle with radius AB

2. Circle with diameter AB

3. Circle with diameter 3AB

4. None of these

Q. If $\omega =\frac{z}{z-\frac{i}{3}}and\left|\omega \right|=1,$ then locus of z is:

Q. Let us write the circular value of an angle formed by the end point of hour hand of a clock in 1 hour rotation.

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.

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

Q.

Describe the locus for questions 1 to 13 given below:

The locus of a point in space, which is always at a distance of 4 cm from a fixed point.

Q. A set of points which satisfy a certain condition is called

1. a locus
2. a circle
3. a triangle
4. none of these

Q. What are coplanar points?

1. Points lying on same line
2. Points lying on same axis
3. Points lying on same object
4. Points lying on same plane

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