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Question

Equation of parabola having the extremities of it’s latus rectum as (3, 4) and (4, 3) is -

  1. open parentheses x minus fraction numerator 7 over denominator 2 end fraction close parentheses to the power of 2 end exponent+ open parentheses y minus fraction numerator 7 over denominator 2 end fraction close parentheses to the power of 2 end exponent= open parentheses fraction numerator x plus y minus 6 over denominator 2 end fraction close parentheses to the power of 2 end exponent    
  2. open parentheses x minus fraction numerator 7 over denominator 2 end fraction close parentheses to the power of 2 end exponent+ open parentheses y minus fraction numerator 7 over denominator 2 end fraction close parentheses to the power of 2 end exponent= fraction numerator left parenthesis x plus y minus 8 right parenthesis to the power of 2 end exponent over denominator 2 end fraction    
  3. open parentheses x minus fraction numerator 7 over denominator 2 end fraction close parentheses to the power of 2 end exponent+ open parentheses y minus fraction numerator 7 over denominator 2 end fraction close parentheses to the power of 2 end exponent= fraction numerator left parenthesis x plus y minus 4 right parenthesis to the power of 2 end exponent over denominator 2 end fraction    
  4. None of these    

The correct answer is: open parentheses x minus fraction numerator 7 over denominator 2 end fraction close parentheses to the power of 2 end exponent+ open parentheses y minus fraction numerator 7 over denominator 2 end fraction close parentheses to the power of 2 end exponent= fraction numerator left parenthesis x plus y minus 8 right parenthesis to the power of 2 end exponent over denominator 2 end fraction


    Focus is open parentheses fraction numerator 7 over denominator 2 end fraction comma fraction numerator 7 over denominator 2 end fraction close parenthesesand it’s axis is the line y = x.
    corresponding value of ‘a’ is fraction numerator 1 over denominator 4 end fraction (square root of 1 plus 1 end root) = fraction numerator square root of 2 over denominator 4 end fraction. Let the equation of its directrix be y + x + λ = 0
    rightwards double arrow fraction numerator vertical line 3 plus 4 plus lambda vertical line over denominator square root of 2 end fraction = 2. fraction numerator square root of 2 over denominator 4 end fraction rightwards double arrow λ = –6, –8.
    Thus equation of parabola is
    open parentheses x minus fraction numerator 7 over denominator 2 end fraction close parentheses to the power of 2 end exponent plus open parentheses y minus fraction numerator 7 over denominator 2 end fraction close parentheses to the power of 2 end exponent=fraction numerator left parenthesis x plus y minus 6 right parenthesis to the power of 2 end exponent over denominator 2 end fraction
    open parentheses x minus fraction numerator 7 over denominator 2 end fraction close parentheses to the power of 2 end exponent plus open parentheses y minus fraction numerator 7 over denominator 2 end fraction close parentheses to the power of 2 end exponent= fraction numerator left parenthesis x plus y minus 8 right parenthesis to the power of 2 end exponent over denominator 2 end fraction.

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