The equation of the common tangent drawn to the curves $y^{2} = 8 x$ and $x y = - 1$ is

y = 2 x + 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 y = x + 6

No worries! We‘ve got your back. Try BYJU‘S free classes today!

y = x + 2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

3 y = 8 x + 2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $y = x + 2$
Tangent to the parabola, $y = m x + \frac{2}{m}$

$\Rightarrow x y = - 1$

$\Rightarrow x (m x + \frac{2}{m}) = - 1$

$\Rightarrow m^{2} x^{2} + 2 x + m = 0$

for this quadratic to have a double root, we need the discriminant to be equal to zero.

$\Rightarrow 4 - 4 m^{2} (m) = 0$

$\Rightarrow m^{3} = 1$

$\Rightarrow m = 1$

Hence the equation of the tangent, $y = x + 2$

Suggest Corrections

Similar questions

x y = - 1

y^{2} = 8 x

The equation of the common tangent to the curves is $y^{2} = 8 x a n d x y = - 1$ is

y^{2} = 8 x and x y = - 1

y^{2} = 8 x a n d x y = - 1

The equation of the common tangent to the curves $y^{2} = 8 x$ and $x y = - 1$ is

Join BYJU'S Learning Program