Question

The equation of a tangent to the hyperbola $3x^2-y^2=3$, parallel to the line $y=2x+4$ is

• A. $y=2x+3$
• B. $y=2x+1$
• C. $y=2x-1$
• D. $y=2x+2$

Answer 1

Answer: (B), (C)

$y=2x-1$
$y=2x+1$

The equation of the hyperbola is
$\frac{x^2}{1}-\frac{y^2}{3}=1$ or $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
where $a^2=1$ and $b^2=3$.
We know $y=mx+c$ is a tangent to the hyperbola if
$c^2=a^2{m}^2-b^2$. Here $m=2$,
$c^2=1$, i.e., $c=\pm 1$.
The required tangents are,
$y=2x-1$ and $y=2x+1$
Hence, options 'B' and 'C' are correct.