# Locus

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• Q1

Write the locus of a point which is equidistant from two parallel lines.

Marks:1

The locus of a point equidistant from two parallel lines is a line parallel to the given lines and midway between them.

• Q2

Check whether the point (2, 3) lies on the locus given by the equation 2x2 + 3y2 - 5x - 8y = 17.

Marks:1

The given equation is: 2x2 + 3y2 – 5x – 8y = 17

Putting x = 2 and y = 3 in LHS of the given equation:

L.H.S. = 2x2 + 3y2 – 5x – 8y
= 2(2)2 + 3(3)2 – 5(2) – 8(3)

= 8 + 27 – 10 – 24

= 35 – 34
= 1, which is not equal to R.H.S.

So, the given point does not lie on the given equation.

• Q3

Find the equation of the locus of a point which moves so that its distance from x-axis is always 4 units.

Marks:1

Let a point P move in a plane such that its distance form the x-axis is always equal to 4 units. The point P will trace out a straight line parallel to x-axis at a distance 4 units above the x-axis. Therefore, the equation of the locus of point P is y = 4.

• Q4

Find the locus of a point which moves so that its distance from the x-axis is thrice its distance from the y-axis.

Marks:2

Let (h, k) be any point on the locus. Then, by the given condition
|k| = 3|h|, [As, |y| = 3|x|]
Therefore, the locus of (h,k) is y = ±3x (where equal distance does not mean equal coordinate.)