Master all past questions related to Loci.
37 questions across all exams
The locus of all points having a distance of l units from each of the two fixed points a and b is
a line parallel to the ab
a line perpendicular to the line ab through the mid-point of ab
a circle through a and b with Centre at the midpoint of ab
a circle with center at a and passes through b
P and Q are fixed points and X is a variable point which moves so that angle PXQ = 45°. What is the locus of X?
A pair of straight lines parallel to PQ
The perpendicular bisector of PQ
An arc of a circle passing through P and Q
A circle with diameter PQ
If U and V are two distinct fixed points and W is a variable point such that UWV is a right angle. What is the locus of W?
The perpendicular bisector of UV
A circle with UV as radius
A line parallel to the line UV
A circle with the line UV as the diameter
What is the locus of the mid-points of all chords of length 6cm within a circle of radius 5cm and with centre O
A circle of radius 4cm and with centre O
The perpendicular bisector of the chords
A straight line passing through center O
A circle of radius 6cm and with centre O
The locus of a point which moves so that it is equidistant from two intersecting straight lines is the
perpendicular bisector of the two lines
angle bisector of the two lines
bisector of the two lines
line parallel to the two lines
The locus of a point which is equidistant from two given fixed points is the
perpendicular bisector of the straight line joining them
parallel line to the straight line joining them
transverse to the straight line joining them
angle bisector of 90° which the straight line joining them makes with the horizontal
What is the locus of a point P which moves on one side of a straight line XY, so that the angle XPY is always equal to 90°
The perpendicular bisector of XY
A right-angled triangle
A circle
A semi-circle
P is on the locus of a point equidistant form two given points X and Y. UV is a straight line through Y parallel to the locus. If ∠PYU is 40° find ∠XPY
100°
80°
50°
40°
The locus of all points at a distance 8 cm from a point N passes through Points T and S. If S is equidistant from T and N, find the area of triangle STN.
4/3cm²
16/3cm²
32cm²
64cm²
P is a point on one side of the straight line UV and P moves in the same direction as UV. If the straight line ST is on the locus of P and ∠VUS = 50°, find ∠UST.
310°
130°
If P and Q are fixed points and X is a point which moves so that XP = XQ, the locus of X is
a straight line
a circle
the bisector ∠PXQ
the perpendicular bisector of PQ
A point P moves such that it is equidistant from the points Q and R. find QR when PR = 8cm and ∠PRQ = 30°
4cm
4/3cm
8cm
8/3cm
Find the locus of a point which moves such that its distance from the line y = 4 is a constant, k.
y = 4 + k
y = k - 4
y = k ± 4
y = 4 ± k
The locus of a point P which is equidistant from two given points S and T is
a perpendicular to ST
a line parallel to ST
the angle bisector of PS and ST
the perpendicular bisector ST
The locus of a point P which moves on one side only of a straight line XY so that ∠XPY = 90° is
the perpendicular bisector of XY
a semicircle
an arc of a circle through X,Y
Find the equation of the locus of a point P(x, y) which is equidistant form Q (0, 0) and R (2, 1).
2x + y = 5
2x + 2y = 5
4x + 2y = 5
4x - 2y = 5
Determine the locus of a point inside a square PQRS which is equidistant from PQ and QR
The diagonal PR
The diagonal QS
Side SR
The locus of a point which is 5cm from the line LM is a
pair of lines on opposite sides of LM and parallel to it each distances 5cm form LM
line parallel LM and 5 cm from LM
pair of parallel lines on one side of LM and parallel to LM
line distance 10cm from LM and parallel to LM
Two lines PQ and ST intersect at 75°. The locus of points equidistant from PQ and ST lies on the
bisector of the angles between lines PQ and ST
bisector of the angles between lines PT and QS
perpendicular bisector of ST
perpendicular bisector of PQ
What is the locus of points equidistant from the line ax + by + c = 0?
A line ax + by + q = 0
A line ax - by + q = 0
A line bx - ay + q = 0
A line bx + ay + q = 0
If the locus of the points which are equidistant from points P and Q meets line PQ at point N, then PN equals
12\frac{1}{2}21 NQ
2NQ
74\frac{7}{4}47 NQ
NQ
A particle P moves between points S and T such that angle SPT is always constant. Find the locus of P
it is a semi-circle with ST as diameter
It is a perpendicular bisector of ST
It is a quadrant of circle with ST as diameter
It is a straight line perpendicular to ST
Find the locus of points equidistant from two straight lines y - 5 = 0 and y - 3 = 0.
y - 2 = 0
y - 4 = 0
y - 1 = 0
y - 3 = 0
The locus of a point equidistant from two points P (6,2) and R (4, 2) is a perpendicular bisector of PR passing through
(2,5)
(5,2)
(1,0)
(0,1)
Find the locus of a particle which moves in the first quadrant so that it is equidistant from the lines x = 0 and y = 0 (where k is constant)
x + y = 0
x - y = 0
x + y + k = 0
x - y - k = 0
What is the locus of the mid-point of all chords of length 6cm with a circle of radius 5cm and with centre O
A circle of radius 4cm and Centre O
A straight line passing through centre O
What is the locus of points that is equidistant from points P (1,3) and Q (3,5)?
y = x - 6
y = x + 6
y = - x - 6
The perpendicular bisector of a line XY is the locus of a point.
whose distance from X is always twice its distance from Y
whose distance from Y is always twice its distance from X
which moves on the line XY
which is equidistant from the points X and Y
The locus of a point equidistant from the intersection of lines 3x - 7y + 7 = 0 and 4x - 6y + 1 = 0 is
line parallel to 7x + 13y + 8 = 0
circle
Semicircle
bisector of the line 7x + 13y + 8 = 0
The locus of the points which is equidistant from the line PQ forms
circle centre P
circle centre Q
pair of parallel lines to PQ
perpendicular line to PQ
The locus of a dog tethered to a pole with a rope of 4m is
A semi-circle with diameter 4m
semi-circle with radius 4m
circle with diameter 4m
circle with radius 4m
How many 222\sqrt{2}22cm diameter discs can be cut out of a sheet of cardboard 2182π/42^{18}\sqrt{2\pi}/42182π/4cm long and 2π/4\sqrt{2\pi}/42π/4cm wide?
4
2192^{19}219
217π3/4(4/2+2)2^{17}\pi^{3/4}(4/2 + 2)217π3/4(4/2+2)
218π5/4(1+22^{18}\pi^{5/4}(1 + \sqrt{2}218π5/4(1+2
The locus of a point which is equidistant from the line PQ forms
pair of parallel lines each opposite to PQ
What is the loci of a distance 4cm from a given point P?
A straight line of length 4cm
a circle of radius 4cm
perpendicular to point P at 4cm
a circle of diameter 4cm
Find the equation of the locus of a point A(x, y) which is equidistant from B(0, 2) and C(2, 1).
4x + 2y = 3
4x - 3y = 1
4x - 2y = 1
4x + 2y = - 1
The locus of point equidistant from two given points is
Parallel bisector of the distance between the points
Perpendicular bisector of the distance between the points
Angular bisector between the line
Transverse bisector of the angle
The locus of points at a given distance from a point X is
angle bisector
perpendicular
A circle with radius X
a circle with centre X
