Question

Find the common :
x^2 + 1 + 2x - 16y^2​

Answer 1

Step-by-step explanation:

Correct option is

A

x+2y+2=0

equation of tangent to the parabola

y

2

=2x is y=mx+

m

2

1

⇒y=mx+

2m

1

_______ (i)

And equation of tangent to the parabola

x

2

=16y is y=mx−4m

2

_________ (ii)

For common tangent, equation (i) and equation (ii) are identical.

∴

2m

1

=−4m

2

⇒m

3

=−

8

1

⇒m=−

2

1

∴ equation of common tangent is

y=−

2

1

x−

2

1

2

1

⇒2y=−x−2

⇒x+2y+2=0