A hyperbola passes through points (3, 2) and (-17, 12) and has its centre at origin and transverse a

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10-2. Parabola, Ellipse, Hyperbola

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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

A

$2$

B

$4$

C

$6$

D

None of these

Solution

(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$.

Standard 11

Mathematics

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