MCQ
If $(a -2)x^2 + ay^2 = 4$ represents rectangular hyperbola, then $a$ equals :-
- A$0$
- B$2$
- ✓$1$
- D$3$
$\Rightarrow$ On simplifying Equation
1, $\frac{x^{2}}{\frac{4}{a-2}}-\frac{y^{2}}{\left(\frac{-4}{a}\right)}=1$
where we see, $a^{2}=\frac{4}{a-2}$ and $b^{2}=\frac{-4}{a}$
If $b^{\prime}=a^{\prime} \Rightarrow b^{\prime 2}=a^{\prime 2}$
$\Rightarrow \frac{-4}{a}=\frac{4}{a-2}$
$\Rightarrow-(a-2)=a$
$\Rightarrow 2=2 a$
$\Rightarrow a=1$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$ 11 x+y+\lambda z=-5 $
$ 2 x+3 y+5 z=3 $
$ 8 x-19 y-39 z=\mu$
has infinitely many solutions, then $\lambda^4-\mu$ is equal to :