Find the (i) lengths of the axes, (ii) coordinates of the vertices \[\frac{{{x}^{2}}}{9}-\frac{{{y}^{2}}}{16}=1\]

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Find the (i) lengths of the axes, (ii) coordinates of the vertices

$\frac{{{x}^{2}}}{9}-\frac{{{y}^{2}}}{16}=1$

Find the (i) lengths of the axes, (ii) coordinates of the vertices

$\frac{{{x}^{2}}}{9}-\frac{{{y}^{2}}}{16}=1$

Given Equation:

$\frac{{{x}^{2}}}{9}-\frac{{{y}^{2}}}{16}=1$

Comparing with the equation of hyperbola

$\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1$

we get,

a = 3 and b = 4

(i) Length of Transverse axis = 2a = 6 units.

Length of Conjugate axis = 2b = 8 units.

(ii)coordinates of the vertices =

$(\pm a,0)=(\pm 3,0)$

i

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