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