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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
A hyperbola passes through the points $(3, 2)$ and $(-17, 12)$ and has its centre at origin and transverse axis is along $x$ - axis. The length of its transverse axis is
  • ✓
    $2$
  • B
    $4$
  • C
    $6$
  • D
    None of these
✓

Answer

Correct option: A.
$2$
a
(a) Let the equation of hyperbola is $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$

But it passes through $(3, 2)$

==> $\frac{9}{{{a^2}}} - \frac{4}{{{b^2}}} = 1$.....$(i)$

Also its passes through $(-17, 12)$

==> $\frac{{{{( - 17)}^2}}}{{{a^2}}} - \frac{{{{(12)}^2}}}{{{b^2}}} = 1$ .....$(ii)$

Solving these, we get $a = 1$ and $b = \sqrt 2 $

Hence length of transverse axis $ = 2a = 2$.

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