Maths-
General
Easy

Question

The locus of the point which moves so that the square of its distance from the point (3, 0) is
equal to 7 is

  1. x2 + y2 = 2    
  2. x2 + y2 – 6x = 0    
  3. x2 + y2 – 6x + 2 = 0    
  4. 3x – 4y – 46 = 0    

hintHint:

We are given that the locus of point moves to keep the square of its distance from the another point constant. The square of the distance is 7. The coordinates of another point is (3,0). We have to find the locus. We will assume the coordinates of the points and use distance formula to find the distance between the point and the given point.

The correct answer is: x2 + y2 – 6x + 2 = 0


    Let the point of which we are going to find the locus be (x,y)
    The given point is (3,0)
    The square of the distance is 7.
    We can find the distance between the two points using distance formula.
    Distance = square root of left parenthesis x space minus space 3 right parenthesis squared plus left parenthesis y space minus 0 right parenthesis squared end root
    Squaring both the sides
    (Distance)2left parenthesis x space minus space 3 right parenthesis squared space plus space left parenthesis y space minus 0 right parenthesis squared
    We already have to value of square of the distance. It is 7.
    Substituting the value we get,
    7 = left parenthesis x space minus space 3 right parenthesis squared space plus space y to the power of 2 end exponent
    Rearranging we get
    left parenthesis x space minus space 3 right parenthesis squared space plus space y to the power of 2 end exponent = 7
    Expanding the bracket
    left parenthesis x space minus space 3 right parenthesis squared space plus space y to the power of 2 end exponent space equals space 7
x squared space minus 6 x space plus space 9 space plus space y squared space equals space 7
x to the power of 2 space end exponent minus 6 x space plus space y squared space plus space 9 space minus space 7 space equals space 0
x to the power of 2 space end exponent minus 6 x space plus space y squared space plus space 2 space equals 0
    This is the required equation.

    Locus of a point means path traced by the given point while satisfying the given conditions. For such questions, we should know distance formula.

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