Locus

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  • Q1

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

    Marks:1
    Answer:

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

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  • Q2

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

    Marks:1
    Answer:

    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.

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  • 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
    Answer:

    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.

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  • 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
    Answer:

    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.)

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  • Q5

    Let C (3, 4) be a fixed point. We know from plane geometry that the locus of the point P such that the distance PC remains constant and is equal to 6 units is a circle with centre C and radius equal to 6 units. Find the equation of locus.

    Marks:2
    Answer:

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