Introduction to LOCI
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The locus of a point equidistant from two parallel lines is
any line parallel to both the lines
a line parallel to both the lines and midway between them
the perpendicular bisector of any one of the parallel lines
any line perpendicular to both the lines
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.
- angle bisector
- area
- angle
What are you doing there? Here ‘there’ is a or an?
verb
adjective
adverb
noun
The locus of mid-points of all parallel chords in a circle is
the diameter of the circle which is perpendicular to the given chords
any chord of the circle
any diameter of the circle
any chord of the circle which is perpendicular to the given chords
A and B are two fixed points. What will be the locus of the point P such that ∠ APB=90∘
The locus of point P is the perpendicular bisector of line joining AB.
The locus of point P is the circumference of a circle with AB as the diameter.
The locus of point P is the circumference of a semi-circle with AB as the diameter.
The locus of P is any circle passing through the points A and B.
Construct ΔPQR with QR = 6.5 cm, PQ= 5.5 cm, PR = 5 cm. Construct and find the radius of incircle of the ΔPQR
3.2 cm
2.8 cm
4.6 cm
1.6 cm
The locus of a point equidistant from two parallel lines is a line parallel to both the lines. State whether true or false.
True
False
The locus of satisfying the inequality , where is
- 4.8
- (1−√1+y2) & (−1−√1+y2)
- (−1−√1−y2) & (−1+√1−y2)
- (1+√1+y2) & (1−√1+y2)
- (−1−√1+y2) & ( −1−√1−y2)
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
the line x=4.
the line x=8.
lines x=4 and x=8.
y-axis.
Which function models the graph below?
X –axis 1 grid = 1 unit
Y –axis 1 grid = 1 unit
y =(x + 2)2+ 4
y = (x - 4)2+ 2
y = (x + 4)2+ 2
y =(x - 4)2 - 2
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.
False
True
Construct a ΔPQR with QR = 8, PQ= 6 PR = 4. Construct the incircle of the triangle and find the radius of the incircle.
4.2 cm
5.4 cm
4 cm
2.2 cm
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.
∠APC
1.5∠APC
1.2∠APC
1.8∠APC
2∠APC
AB is a fixed line. State the locus of the point P so that AB2= AP2+ BP2
Circle with radius AB
Circle with diameter AB
Circle with diameter 3AB
None of these
What is the locus of the centre of a cycle wheel?
Curved path
Concentric circle
Line diagonal to the ground
Straight line parallel to the ground
The locus of a point P with ∠ APB as 90∘ will be a circle if AB is the diameter.
True
False
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.
- a locus
- a circle
- a triangle
- none of these
- Points lying on same line
- Points lying on same axis
- Points lying on same object
- Points lying on same plane
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
the line y=-4
the line y=6
the line y=-5 and the line y=-7
x - axis