If S \equiv \frac{x^2}{k-7}+\frac{y^2}{11- {\k}}-1=0, {\k} \in {\R}-\{7,11\}, then which one of the following statements is incorrect?

Correct Answer is : S=0 represents a hyperbola with eccentricity √32, when k=13

{\S}=0 represents a circle with radius \sqrt{2}, when {\k}=9

{\S}=0 represents an ellipse with eccentricity \sqrt{\frac{2}{3}}, when {\k}=10

{\S}=0 represents a hyperbola with eccentricity \sqrt{\frac{6}{5}}, when {\k}=12

S=0 represents a hyperbola with eccentricity \sqrt{\frac{3}{2}}, when {\k}=13

AP EAPCET 15th May 2023 Shift 2 Solved Paper

Section: Mathematics

Question : 58 of 160

Marks: +1, -0

If S≡‌

k−7

+‌

11−k

−1=0,k∈R−{7,11}, then which one of the following statements is incorrect?

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