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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
${x^2} - 4{y^2} - 2x + 16y - 40 = 0$ represents
  • A
    A pair of straight lines
  • B
    An ellipse
  • ✓
    A hyperbola
  • D
    A parabola
✓

Answer

Correct option: C.
A hyperbola
c
(c) ${x^2} - 2x - 4{y^2} + 16y - 40 = 0$

==> $({x^2} - 2x) - 4({y^2} - 4y) - 40 = 0$

==> ${(x - 1)^2} - 1 - 4[{(y - 2)^2} - 4] - 40 = 0$

==> ${(x - 1)^2} - 4{(y - 2)^2} = 25$

==> $\frac{{{{(x - 1)}^2}}}{{25}} - \frac{{{{(y - 2)}^2}}}{{25/4}} = 1$, which is a hyperbola.

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