Question

For the conic $9x^2-16y^2+18x+32y-151=0$, find $e$.

• A. $\frac{5}{4}$
• B. $\frac{4}{5}$
• C. $\frac{1}{2}$
• D. None of these

Answer 1

The correct option is A $\frac{5}{4}$

The given equation can be written as
$9(x^2+2x)-16(y^2-2y)=151$ or $9(x^2+2x+1)-16(y^2-2y+1)=151+9-16=144$
or $\frac{{(x+1)}^2}{16}-\frac{{(y-1)}^2}{9}=1$ or $\frac{X^2}{16}-\frac{Y^2}{9}=1$ where $X=x+1,Y=y-1,a^2=16,b^2=9$
Centre is $X=0,Y=0,i.e.(-1,1),b^2=a^2(e^2-1)\therefore e=\frac{5}{4}$