Equation of axis of given hyperbola frac{{{x^2}}}{3} - frac{{{y^2}}}{2} = 1 which is equally incline

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10-2. Parabola, Ellipse, Hyperbola

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Find the equation of axis of the given hyperbola $\frac{{{x^2}}}{3} - \frac{{{y^2}}}{2} = 1$ which is equally inclined to the axes

A

$y = x + 1$

B

$y = x - 1$

C

$y = x + 2$

D

$y = x - 2$

Solution

(a) $\frac{{{x^2}}}{3} – \frac{{{y^2}}}{2} = 1$

Equation of tangent are equally inclined to the axis

$i.e.$, $\tan \theta = 1 = m$.

Eq. of tangent $y = mx + \sqrt {{a^2}{m^2} – {b^2}} $

Given eq. $\frac{{{x^2}}}{3} – \frac{{{y^2}}}{2} = 1$ is a eq. of hyperbola

which is of form $\frac{{{x^2}}}{{{a^2}}} – \frac{{{y^2}}}{{{b^2}}} = 1$.

Now, on comparing ${a^2} = 3$, ${b^2} = 2$

$y = 1.x + \sqrt {3 \times {{(1)}^2} – 2} $

==> $y = x + 1$.

Standard 11

Mathematics

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