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CDS - Locus Test 1181
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CDS - Locus Test 1181
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  • Question 1/5
    1 / -0.33
    A particle is moving in a plane in such a way that, it’s distances from two fixed point are always same. The path thus formed by the particle is:
    Solutions

    Let  and  are two fixed points and  is the co-ordinate of position of moving particle at any time. Then, according to question,

    Since the particle is always at equidistant from both points, it must pass through the midway of line joining two fixed points AB. Since particle is always moving it must be the perpendicular bisector of AB.

  • Question 2/5
    1 / -0.33
    If a point P moves such that the sum of the squares of its distances from two fixed points A and B is a constant, then the locus of the point P is
    Solutions
    The locus is a circle.
    Standard equation of circle is
    where is centre & is the radius of circle.
  • Question 3/5
    1 / -0.33
    What is the locus of centres of circles which touch a given line at a given point ?
    Solutions

    As OP, O’P, O”P are the radii of the circles touching line T at P, it is perpendicular to the given line.
    OP, O’P, O”P represent the same straight line passing through P and Perpendicular to PT
    Hence the locus of the centre of circles which touch a given line at a given point is a straight line to the given line at the given point.
  • Question 4/5
    1 / -0.33
    Let A and B be two points. What is the locus of the point P such that angle APB = 900?
    Solutions
    As angle formed in a semi-circle is a right angle, hence the point P should be the circumference of a circle with AB as its diameter.
  • Question 5/5
    1 / -0.33
    If the coordinate of a variable point P  where  is a variable quantity.Then find locus of P.
    Solutions

     Let P(h,k) is the variable point. So we can write

    ⇒

    Squaring and adding both side

    ⇒

    Now replace h by x & k by y

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