Question

The equation of the directrices of the hyperbola \(3 x^{2}-3 y^{2}-18 x+12 y+2=0\) is
(A) \(x=3 \pm \sqrt{\frac{13}{6}}\)
(B) \(x=3 \pm \sqrt{\frac{6}{13}}\)
(C) \(x=6 \pm \sqrt{\frac{13}{3}}\)
(D) \(x=6 \pm \sqrt{\frac{3}{13}}\)

Answer 1

Ans : (A)
Hint \(: 3 x^{2}-3 y^{2}-18 x+12 y+2=0 \Rightarrow \frac{(x-3)^{2}}{\left(\sqrt{\frac{13}{3}}\right)^{2}}-\frac{(y-2)^{2}}{\left(\sqrt{\frac{13}{3}}\right)^{2}}=1\)
Here \(a=b=\sqrt{\frac{13}{3}}\) and \(e=\sqrt{2} \therefore\) the equations of the directrices are \(x=3 \pm \sqrt{\frac{13}{6}}\)

Answer 2

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