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STD 11 - 10.2 parabola,ellipse,hyperbola — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 10.2 parabola,ellipse,hyperbola1 Mark
MCQ
The equation ${x^2} - 2xy + {y^2} + 3x + 2 = 0$ represents
  • ✓
    A parabola
  • B
    An ellipse
  • C
    A hyperbola
  • D
    A circle
✓

Answer

Correct option: A.
A parabola
a
(a) $\Delta = (1)\,(1)\,(2) + 2\,\left( {\frac{3}{2}} \right)\,(0)( - 1) - (1)\,{(0)^2} - $$(1)\,{\left( {\frac{3}{2}} \right)^2} - 2{( - 1)^2}$

$ = 2 - \frac{9}{4} - 2 < 0$ and ${h^2} - ab = 1 - 1 = 0$.

i.e., ${h^2} = ab$ ==> a parabola.

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