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NDA 2 2024 Maths, question 57

Topic: Analytical geometry

Q57

The foci of the ellipse 4x2+9y2=14x^{2}+9y^{2}=1 are at QQ and RR. If P(x,y)P(x,y) is any point on the ellipse, then what is PQ+PRPQ+PR equal to?

  1. (a) 22
  2. (b) 11Correct answer
  3. (c) 2/32/3
  4. (d) 1/31/3

Solution.

Answer: (b) 11

  1. Write the ellipse as x²/(1/4)+y²/(1/9)=1.
  2. Its semi-major axis is a=1/2.
  3. By the defining focus property of an ellipse, PQ+PR=2a=1 for every point P on it.