VITEEE 2012 Paper

x2

a2

+

y2

b2

= 1 ...(i)
On differentiating w.r.t. x, we get

2x

a2

+

2y

b2

.

dy

dx

= 0
⇒

dy

dx

= -

xb2

a2y

and x2−y2 = c2
On differentiating w.r.t. x, we get
2x - 2y

dy

dx

= 0
⇒

dy

dx

=

x

y

The two curves will cut at right angles, if
(

dy

dx

)c1 × (

dy

dx

)c2 = - 1
⇒ -

b2x

a2y

.

x

y

= - 1
⇒

x2

a2

=

y2

b2

⇒

x2

a2

=

y2

b2

=

1

2

[using eq. (i)]
On substituting these values in x2−y2 = x2 , we get

a2

2

−

b2

2

= c2
a2−b2 = 2c2