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Conic Sections — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsConic Sections2 Marks
MCQ
The equation $x=\frac{ e^t+ e^{-t}}{2}, y=\frac{ e^t- e^{-t}}{2}, t \in R$,represents represents
  • A
    an ellipse
  • B
    a parabola
  • ✓
    a hyperbola
  • D
    a circle
✓

Answer

Correct option: C.
a hyperbola
(C)
$2 x=e^{t}+e^{-t} \text { and } 2 y=e^{t}-e^{-t}$
$\Rightarrow 4 x^2=e^{2 t}+2+e^{-2 t} \quad\ldots(i)$
$\text {and } 4 y^2=e^{2 t}-2+e^{-2 t} \quad\ldots(ii)$
Subtracting (ii) from (i), we get
$4 x^2-4 y^2=4$
$\Rightarrow x^2-y^2=1$
The equation represents hyperbola.

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