For the hyperbola $16 x^{2} - 9 y^{2} + 32 x + 36 y - 164 = 0$ , find $2 (a + b)$ .

8

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Solution

The correct option is A $14$
Given hyperbola can be written as

$16 x^{2} + 32 x + 16 - 9 y^{2} + 36 y - 36 = 144$
$\frac{(x + 1)^{2}}{9} - \frac{(y - 2)^{2}}{16} = 1$
$\Rightarrow a = 3, b = 4$
Length of major axis $= 2 \times 4 = 8$ and length of minor axis $= 2 \times 3 = 6$ .

Hence sum is $2 (a + b) = 2 (3 + 4) = 14.$

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For the hyperbola 16x2−9y2+32x+36y−164=0, find 2(a+b).

The correct option is A 14Given hyperbola can be written as16x2+32x+16−9y2+36y−36=144(x+1)29−(y−2)216=1⇒a=3,b=4Length of major axis =2×4=8 and length of minor axis =2×3=6. Hence sum is 2(a+b)=2(3+4)=14.

For the hyperbola $16 x^{2} - 9 y^{2} + 32 x + 36 y - 164 = 0$ , find $2 (a + b)$ .