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10.2 parabola,ellipse,hyperbola — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS10.2 parabola,ellipse,hyperbola1 Mark
MCQ
The equation $\frac{{{x^2}}}{{1 - r}} - \frac{{{y^2}}}{{1 + r}} = 1,\;r > 1$ represents
  • A
    An ellipse
  • B
    A hyperbola
  • C
    A circle
  • ✓
    An imaginary ellipse
✓

Answer

Correct option: D.
An imaginary ellipse
d
(d) $\frac{{{x^2}}}{{1 - r}} - \frac{{{y^2}}}{{1 + r}} = 1$, where $r > 1$

or $\frac{{{x^2}}}{{ - p}} - \frac{{{y^2}}}{q} = 1,\,\,\,1 - r = - p$ $(say)$ or $\frac{{{x^2}}}{{ - p}} + \frac{{{y^2}}}{{ - q}} = 1$ i.e., imaginary ellipse with imaginary major and minor axes.

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