Maths-
General
Easy

Question

AB is a chord of the circle x to the power of 2 end exponent plus y to the power of 2 end exponent minus 7 x minus 4 equals 0. If (1, -1) is the mid point of the chord AB then the area of the triangle formed by AB and the coordinate axes is

  1. 9 divided by 20    
  2. 9 divided by 10
             
  3. 3 divided by 20    
  4. 1 divided by 5    

The correct answer is: 9 divided by 20


    The locus of mid points of chords of x to the power of 2 end exponent plus y to the power of 2 end exponent equals a to the power of 2 end exponent which subtend a right angle 120 to the power of 0 end exponent at the centre is
    fraction numerator 1 over denominator 2 end fraction equals fraction numerator square root of left parenthesis x subscript 1 end subscript minus 0 right parenthesis to the power of 2 end exponent plus left parenthesis y subscript 1 end subscript minus 0 right parenthesis to the power of 2 end exponent end root over denominator a end fraction
    a to the power of 2 end exponent equals 4 x subscript 1 end subscript to the power of 2 end exponent plus 4 y subscript 1 end subscript to the power of 2 end exponent
    x.1 plus y open parentheses negative 1 close parentheses minus fraction numerator 7 over denominator 2 end fraction open parentheses x plus 1 close parentheses minus 4 equals 1 to the power of 2 end exponent plus open parentheses negative 1 close parentheses to the power of 2 end exponent minus 7.1 minus 4
    2 x minus 2 y minus 7 x minus 7 equals negative 10
    negative 5 x minus 2 y plus 3 equals 0 rightwards double arrow 5 x plus 2 y minus 3 equals 0
    triangle equals fraction numerator c to the power of 2 end exponent over denominator 2 open vertical bar a b close vertical bar end fraction equals fraction numerator 9 over denominator 2 open vertical bar 5.2 close vertical bar end fraction equals fraction numerator 9 over denominator 20 end fraction

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