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JEE Main
Exam
JEE Main
Subject
Mathematics
Chapter
Hyperbola

JEE Main · Mathematics · Hyperbola

The distance between the foci of the hyperbola x^2-3 y^2-4 x-6...

The distance between the foci of the hyperbola x2−3y2−4x−6y−11=0x^2-3 y^2-4 x-6 y-11=0 is

Options

  1. A44
  2. B66
  3. C88
  4. D1010

Correct answer

C. 88

Step-by-step solution

Given, equation of hyperbola is x2−3y2−4x−6y−11=0⇒(x2−4x+4)−3(y2+2y+1)−11=4−3⇒(x−2)2−3(y+1)2=12⇒(x−2)212−(y+1)24=1 Now, \quade=1+412=23\begin{gathered}x²-3 y²-4 x-6 y-11=0 \\ \Rightarrow \quad\left(x^2-4 x+4\right)-3\left(y^2+2 y+1\right)-11 \\ =4-3 \\ \Rightarrow \quad(x-2)^2-3(y+1)^2=12 \\ \Rightarrow \quad \frac{(x-2)^2}{12}-\frac{(y+1)^2}{4}=1 \\ \text { Now, } \quade=\sqrt{1+\frac{4}{12}}=\frac{2}{\sqrt{3}} \end{gathered}Now, e=1+412=23∴\sqrt{1+\frac{4}{12}}=\frac{2}{\sqrt{3}}\therefore Distance between foci =2 a e=2 ×12×23=\times \sqrt{12} \times \frac{2}{\sqrt{3}}=8
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