JEE Mains Model Paper 2

The slope of the tangent is

dy

dx

=

2ax+3x2

6y2

And the value of this slope at (a,a) is 5/6. Therefore, the equation
y - a =

5

6

(x - a)
⇒

x

− a 5

+

y

a 6

= 1
Represents the tangent. Thus the x intercept α is -a/5 and the y intercept is a/6. From α2+β2 = 61 we now get

a2

25

+

a2

36

= 61
⇒ a2 = 25 × 36
⇒ a = ± 30