Question

The equation of a hyperbola is given in its standard form as $16x^2-9y^2=144$.Equations of directrices is

• A. $5x\pm 16=0$
• B. $5y\pm 16=0$
• C. $5x\pm 12=0$
• D. $5y\pm 12=0$

Answer 1

The correct option is B $5y\pm 16=0$

$Given:16x^2-9y^2=144Or,\frac{x^2}{9}-\frac{y^2}{16}=1Weknow,be=\sqrt{a^2+b^2}\because (b>a)Or,be=\sqrt{9+16}Or,be=\pm 5Or,\frac{b}{e}=\frac{16}{\pm 5}Weknowequationofdirectrixisy=\frac{b}{e}\therefore 5y\pm 16=0$

Option [B]