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Normal to the ellipse fraction numerator x to the power of 2 end exponent over denominator 84 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 49 end fraction equals 1 intersects the major and minor axis at P and Q respectively then locus of the point dividing segment PQ in 2 : 1 is -

  1. fraction numerator 64 x to the power of 2 end exponent over denominator 25 end fraction plus fraction numerator 49 y to the power of 2 end exponent over denominator 100 end fraction equals 1    
  2. fraction numerator 64 x to the power of 2 end exponent over denominator 100 end fraction plus fraction numerator 49 y to the power of 2 end exponent over denominator 25 end fraction equals 1    
  3. 64 x to the power of 2 end exponent plus 49 y to the power of 2 end exponent equals 225  
  4. fraction numerator 49 x to the power of 2 end exponent over denominator 100 end fraction plus fraction numerator 64 y to the power of 2 end exponent over denominator 25 end fraction equals 1  

The correct answer is: fraction numerator 64 x to the power of 2 end exponent over denominator 25 end fraction plus fraction numerator 49 y to the power of 2 end exponent over denominator 100 end fraction equals 1


    Equation of normal 8x sectheta – 7y cosectheta = 15
    P open parentheses fraction numerator 15 over denominator 8 end fraction cos invisible function application theta comma 0 close parentheses, Q open parentheses 0 comma fraction numerator negative 15 over denominator 7 end fraction sin invisible function application theta close parentheses

    3h = fraction numerator 15 over denominator 8 end fraction cos invisible function application theta, 3k = negative fraction numerator 30 over denominator 7 end fraction sin invisible function application theta
    costheta = fraction numerator 8 h over denominator 5 end fraction, sintheta = fraction numerator negative 7 k over denominator 10 end fraction
    hence locus fraction numerator 64 x to the power of 2 end exponent over denominator 25 end fraction plus fraction numerator 49 y to the power of 2 end exponent over denominator 100 end fraction = 1

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