Question

If the line 2x + √(6)y = 2 touches the hyperbola x2 – 2y2 = 4 then the point of contact is

(a) [4, – √6]

(b) [– 5, 2√6]

(c) [(1/2), (1/√6)]

(d) [2, √6]

Answer 1

The correct option (a) [4, – √6]

Explanation:

angent to x2 – 2y2 = 4 at point

(x1, y1) is xx1 – 2yy1 = 4 ....(1)

given tangent is 2x + √(6)y = 2

i.e. 4x + 2√(6)y = 4 .....(2)

from (1) & (2),

x1= 4 and y1 = – √6

∴ required point of contact is [4, – √6].