Question 1: Find the locus of a point equidistant from the point and the y-axis.
Answer:
Let be the point which is equidistant from point
and y-axis.
Distant of point from y-axis is
.
Question 2: Find the equation of the locus of a point which moves such that the ratio of its distances from .
Answer:
be the point which moves such that the ratio of its distances from
Question 3: A point moves as so that the difference of its distances from , prove that the equation to its locus
.
Answer:
be the point.
Squaring both sides we get
Squaring once again we get
Question 4: Find the locus of a point such that the sum of its distances from .
Answer:
be the point such that the sum of its distances from
.
Squaring both sides
Squaring once again we get
Question 5: Find the locus of a point which is equidistant from and x-axis.
Answer:
and x-axis. Let
be the point.
Question 6: Find the locus of a point which moves such that its distance from the origin is three times its distance from x-axis.
Answer:
Let be the point. The distance of
from x-axis is
Question 7: are two fixed points; find the equation to the locus of a point
which moves so that the area of the
units.
Answer:
be the point.
Area of
Therefore or
or
or
Question 8: Find the locus of a point such that the line segments having end points subtend a right angle at that point.
Answer:
be the point such that
Question 9: If are two fixed points, find the locus of a point
so that the area of
sq. units.
Answer:
be the point.
or
or
or
Question 10: A rod of length slides between the two perpendicular lines. Find the locus of the point on the rod which divides it in the ratio
.
Answer:
Let axis be the two perpendicular lines.
Let be the two intercepts on the axes.
Let be the point that divides
in
ratio.
Now
Question 11: Find the locus bf the mid-point of the portion of the line which is intercepted between the axes.
Answer:
Given line is
Let be th emid point of
We know
Question 12: If is the origin and
is a variable point on
. Find the locus of the mid-point of
.
Answer:
Let be
. It lies on
… … … … … i)
Let be the mid point of
Substituting in i) we get