Question

The number of tangents to the

hyperbola 2 a² y² b² = 1 parallel to

X-axis are​

Answer 1

Answer:

Step-by-step explanation:

Equation  of  line  through  (b,a)  is  

y−a=m(x−b)

y=mx+(a−mb)

Condition  for  line  y=mx+c  to  be  a  tangent  to  hyperbola  is c  

2

=a  

2

m  

2

−b  

2

 

⇒(a−mb)  

2

=a  

2

m  

2

−b  

2

 

⇒a  

2

+m  

2

b  

2

−2amb=a  

2

m  

2

−b  

2

 

m  

2

(b  

2

−a  

2

)−2abm+a  

2

+b  

2

=0

⇒m  

1

​

m  

2

​

=tanθ  

1

​

tanθ  

2

​

=  

b  

2

−a  

2

 

a  

2

+b  

2

 

​

=2

⇒b  

2

−a  

2

=  

2

a  

2

+b  

2

 

​