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Conic Sections — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsConic Sections2 Marks
MCQ
The parametric representation $\left(2+t^2, 2 t+1\right)$ represents
  • A
    a parabola with focus (1, 2)
  • ✓
    a parabola with vertex (2, 1)
  • C
    a parabola with vertex (0, 0)
  • D
    a parabola with vertex (1, 2)
✓

Answer

Correct option: B.
a parabola with vertex (2, 1)
(B)
$x=2+t^2$ and $y=2 t+1$
$\Rightarrow t ^2=(x-2)$ and $t ^2=\left(\frac{y-1}{2}\right)^2=\frac{(y-1)^2}{4}$
$\Rightarrow \frac{(y-1)^2}{4}=(x-2) \Rightarrow(y-1)^2=4(x-2)$
$\therefore$ Vertex is $(2,1)$

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