Search any question & find its solution
Question:
Answered & Verified by Expert
If the point $(1,1)$ and the origin lie in the same region with respect to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{1}=1(a>0)$, then the range of a is
Options:
Solution:
2587 Upvotes
Verified Answer
The correct answer is:
$\left(\frac{1}{\sqrt{2}}, \infty\right)$
Since centre of given hyperbola is $(0,0)$ Given that origin and $(1,1)$ lie in same region therefore $(1,1)$ lie inside the hyperbola.
$\begin{aligned}
& \therefore \frac{1}{a^2}-1-1 < 0 \Rightarrow \frac{2 a^2-1}{a^2} < 0 \Rightarrow a>\frac{1}{\sqrt{2}} \\
& \therefore a \in\left(\frac{1}{\sqrt{2}}, \infty\right)
\end{aligned}$
$\begin{aligned}
& \therefore \frac{1}{a^2}-1-1 < 0 \Rightarrow \frac{2 a^2-1}{a^2} < 0 \Rightarrow a>\frac{1}{\sqrt{2}} \\
& \therefore a \in\left(\frac{1}{\sqrt{2}}, \infty\right)
\end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.