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Conic Sections — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsConic Sections2 Marks
MCQ
The co-ordinates of a point on $2 y^2=7 x$ whose parameter is -2 are
  • ✓
    $\left(\frac{7}{2},-\frac{7}{2}\right)$
  • B
    $\left(\frac{1}{2}, \frac{1}{3}\right)$
  • C
    (1,-2)
  • D
    (1,-3)
✓

Answer

Correct option: A.
$\left(\frac{7}{2},-\frac{7}{2}\right)$
(A)
Given $t=-2$
$2 y^2=7 x$
$\Rightarrow y^2=\frac{7}{2} x$
Comparing with $y^2=4 a x$, we get
$4 a=\frac{7}{2} \Rightarrow a=\frac{7}{8}$
∴ the point is
$P=\left(a t^2, 2 a t\right)=\left(\frac{7}{8} \times 4,2 \times \frac{7}{8} \times(-2)\right)$
$\therefore \quad P =\left(\frac{7}{2}, \frac{-7}{2}\right)$

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