Find the equation of the hyperbola whose Focus is at (4, 2) centr…

Question

Find the equation of the hyperbola whose
Focus is at (4, 2) centre at (6, 2) and e = 2.

✓

Answer

The equation of the hyperbola with centre (X₀, Y₀) is given by
$\frac{\text{(x}-\text{x}_0)}{\text{a}^{2}}-\frac{(\text{y}-\text{y}_0)^{2}}{\text{b}^{2}}=1$
Focus = $(\text{ae}+\text{x}_0, \text{y}_0)$
$\therefore\text{ae} = -2$
$\Rightarrow\text{a} = -1$
$\text{b}^{2} = (-2)^{2}-\text{a}^{2}$
$\Rightarrow\text{b}^{2}=(-2)^{2}-(-1)^{2}$
$\Rightarrow\text{b}^{2}=3$
$\Rightarrow\frac{\text{(x}-6)^{2}}{1}-\frac{(\text{y}-2)^{2}}{3}=1$
$\Rightarrow3\text{(x}-6)-(\text{y}-2)^{2}=3$

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