Maths-
General
Easy

Question

If P identical to left parenthesis x comma   y right parenthesis, F subscript 1 end subscript identical to left parenthesis 3 comma   0 right parenthesis, F subscript 2 end subscript identical to left parenthesis negative 3 comma   0 right parenthesis and 16 x to the power of 2 end exponent plus 25 y to the power of 2 end exponent equals 400, then P F subscript 1 end subscript plus P F subscript 2 end subscript equals

  1. 8    
  2. 6    
  3. 10    
  4. 12    

The correct answer is: 10


    Equation of the curve is fraction numerator x to the power of 2 end exponent over denominator 5 to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator 4 to the power of 2 end exponent end fraction equals 1
    Þnegative 5 less or equal than x less or equal than 5 comma negative 4 less or equal than y less or equal than 4
    P F subscript 1 end subscript plus P F subscript 2 end subscript equals square root of left square bracket left parenthesis x minus 3 right parenthesis to the power of 2 end exponent plus y to the power of 2 end exponent right square bracket end root plus square root of left square bracket left parenthesis x plus 3 right parenthesis to the power of 2 end exponent plus y to the power of 2 end exponent right square bracket end root
    equals square root of left parenthesis x minus 3 right parenthesis to the power of 2 end exponent plus fraction numerator 400 minus 16 x to the power of 2 end exponent over denominator 25 end fraction end root plus square root of left parenthesis x plus 3 right parenthesis to the power of 2 end exponent plus fraction numerator 400 minus 16 x to the power of 2 end exponent over denominator 25 end fraction end root
    equals fraction numerator 1 over denominator 5 end fraction open curly brackets square root of left parenthesis 9 x to the power of 2 end exponent plus 625 minus 150 x right parenthesis end root plus square root of left parenthesis 9 x to the power of 2 end exponent plus 625 plus 150 x right parenthesis end root close curly brackets
    equals fraction numerator 1 over denominator 5 end fraction open curly brackets square root of left parenthesis 3 x minus 25 right parenthesis to the power of 2 end exponent end root plus square root of left parenthesis 3 x plus 25 right parenthesis to the power of 2 end exponent end root close curly brackets equals fraction numerator 1 over denominator 5 end fraction open curly brackets 25 minus 3 x plus 3 x plus 25 close curly brackets
    equals 10, left parenthesis because 25 minus 3 x greater than 025 plus 3 x greater than 0)

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