Eccentricity of the hyperbola $16x^2 - 3y^2 - 32x - 12y - 44 = 0$ is A) $\sqrt{17}/3$ B) $\sqrt{19}/3$ C) $\sqrt{19}/3$ D) $\sqrt{17}/3$

Eccentricity of the hyperbola 16x² - 3y² - 32x - 1 – Class 11 Mathematics

Miscellaneous Exercise 7(I) · Q111

16x^2 - 3y^2 - 32x - 12y - 44 = 0

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$16x^2-3y^2-32x-12y-44=0$ .

Group: $16(x^2-2x)-3(y^2+4y)=44$ .

Complete the square: $16(x^2-2x+1-1)-3(y^2+4y+4-4)=44$

$\Rightarrow 16(x-1)^2-16-3(y+2)^2+12=44$

$\Rightarrow 16(x-1)^2-3(y+2)^2=48$ .

Divide by 48: $\dfrac{(x-1)^2}{3}-\dfrac{(y+2)^2}{16}=1$ . So $a^2=3,\,b^2=16$ . …