TS EAMCET 04 May 2019 Shift 2 Solved Paper

The line 2x+y−1=0 is tangent to the hyperbola ‌

x2

a2

−‌

y2

b2

=1
The equation of direction is x=‌

a

e

Therefore, the point (‌

a

e

,0) passes through the line
2x+y+1=0
2(‌

a

e

)+0=1
2a=e
2a2=ae
Also,
(ae)2=a2+b2
Therefore,

4a4=a2+b2
The equation of tangent is,
y=mx±√a2m2−b2
Therefore,
a2(2)2−b2‌‌=1
4a2−b2‌‌=1
On solving,
a=1,‌

1

2

Therefore,
e‌‌=2a
‌‌=2(1)
‌‌=2