Question

If x = 9 is the chord of the hyperbola x² – y² = 9 then the equation of the corresponding pair of tangents at the end points of the chord is ..........

(a) 9x² – 8y² + 18x – 9 = 0

(b) 9x² – 8y² – 18x + 9 = 0

(c) 9x² – 8y² – 18x – 9 = 0

(d) 9x² – 8y² + 18x + 9 = 0

Answer 1

 The correct option (b) 9x² – 8y² – 18x + 9 = 0

Explanation:

Let pair of tangent from point (x₁, y₁) to hyperbola x² – y² = 9 is drawn.

Then chord of contact will be xx₁ – yy₁ = 9   ....(1)

but given chord of contact is x = 9 .....(2)

as (1) & (2) represents same line, by comparing x₁ = 1 and y₁ = 0.

∴ pair of tangents drawn from (1, 0) to x² – y² = 9 is 

(x² – y² – 9)( 12 – 02 – 9) = (1x – 0y – 9)² using SS₁ = T²

∴  (x² – y² – 9)(– 8) = (x – 9)²

∴   – 8x² + 8y² + 72 = x² – 18x + 81

∴   9x² – 8y² – 18x + 9 = 0.