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 .

Hence the locus of is

Question 2: Find the equation of the locus of a point which moves such that the ratio of its distances from and is .

Answer:

Given . Let be the point which moves such that the ratio of its distances from and is

Given

Hence the locus of is

Question 3: A point moves as so that the difference of its distances from and is , prove that the equation to its locus , where .

Answer:

Given and is . Let be the point.

Squaring both sides we get

Squaring once again we get

Hence locus of is where

Question 4: Find the locus of a point such that the sum of its distances from and is .

Answer:

Given and . Let be the point such that the sum of its distances from and is .

Squaring both sides

Squaring once again we get

Hence the locus of is

Question 5: Find the locus of a point which is equidistant from and x-axis.

Answer:

Given and x-axis. Let be the point.

Hence the locus of is

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

Hence the locus of is

Question 7: are two fixed points; find the equation to the locus of a point which moves so that the area of the is units.

Answer:

Given . Let be the point.

Area of

Therefore or

or

Hence the locus of or

Question 8: Find the locus of a point such that the line segments having end points and subtend a right angle at that point.

Answer:

Given and . Let be the point such that

Hence the locus of is

Question 9: If and are two fixed points, find the locus of a point so that the area of sq. units.

Answer:

Given and . Let be the point.

Therefore are of

or

or

Hence the locus of is 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 and axis be the two perpendicular lines.

Let and be the two intercepts on the axes.

Let be the point that divides in ratio.

and

Now

Hence locus of is

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

When

When

Let be th emid point of

We know

Hence the locus of is

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

and

and

Substituting in i) we get

Hence the locus of is