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AP EAMCET202315 May 2023Evening ShiftMathematicsHyperbolaActual

If S X ^2 k -7 + y ^2 11- k -1=0, k R - 7,11 , then which one of the following statements is incorrect?

Options

  1. AS =0 represents a circle with radius 2 , when k =9
  2. BS=0 represents an ellipse with eccentricity 2 3 , when k =10
  3. CS=0 represents a hyperbola with eccentricity 6 5 when k =12
  4. DS=0 represents a hyperbola with eccentricity 3 2 when k =13

Correct answer

C. S=0 represents a hyperbola with eccentricity 6 5 when k =12

Step-by-step solution

Given that S= x^2 k-7 + y^2 11-k -1=0...(i) Put k=13 x^2 6 - y^2 2 -1=0 x^2 6 - y^2 2 =1 Represent equation of hyperbola, where a^2=6 and b^2=2 . Now, e= 1+ b^2 a^2 = 1+ 2 6 = 2 3 Put k=12 , we get x^2 5 - y^2 1 =1 Represent equation of hyperbola where a^2=5 and b^2=1 . Now, e= 1+ b^2 a^2 = 1+ 1 5 = 6 5 .

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