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The equation of the hyperbola with its transverse axis is parallel to x-axis, and its centre is $(3, - 2)$ , the length of axes 8, 6 is

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$\frac{{(x - 3)}^{2}}{16} - \frac{{(y + 2)}^{2}}{9} = 1$

$\frac{{(x + 2)}^{2}}{25} - \frac{{(y - 1)}^{2}}{11} = 1$

$\frac{{(x - 2)}^{2}}{16} - \frac{{(y - 2)}^{2}}{19} = 1$

$\frac{{(x - 3)}^{2}}{6} - \frac{{(y - 2)}^{2}}{9} = 1$

answer is A.

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Detailed Solution

: Centre $(α, β) = (3, - 2)$

Length of transverse axis $= 2 a = 8 \Rightarrow a = 4 a$

Length of conjugate axis $= 2 b = 6 \Rightarrow b = 3$

$∴$ Equation of hyperbola is $\frac{{(x - 3)}^{2}}{16} - \frac{{(y + 2)}^{2}}{9} = 1$

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