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Conic Sections — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsConic Sections2 Marks
MCQ
The equation $\frac{x^2}{12-k}+\frac{y^2}{8-k}=1$ represents
  • A
    a hyperbola if k < 8
  • B
    an ellipse if k > 8
  • ✓
    a hyperbola if 8 < k < 12
  • D
    none of these
✓

Answer

Correct option: C.
a hyperbola if 8 < k < 12
(C)
$\begin{array}{l}\frac{x^2}{12-k}+\frac{y^2}{8-k}=1 \\\Rightarrow \frac{x^2}{12-k}-\frac{y^2}{k-8}=1 \\\therefore12>k \text { and } k>8 \\\Rightarrow 8 < k < 12\end{array}$
$\therefore$ the given equation represents a hyperbola, if $8 < k< 12$.

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