If x - 2y + k = 0 is a common tangent to y² = 4x & = 1 (a > √3), then the value of a, k and other common tangent are given by -

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If x - 2y + k = 0 is a common tangent to y2 = 4x & = 1 (a > &#8730;3), then the value of a, k and other common tangent are given by -

Accepted Answer

Given slope of common tangent m =
Equation of general tangent to y² = 4x is
y = mx +       ...... (i)
⇒ y = x + 2      [∴ m = in given equation]
On comparing with given equation,
we get k = 4
Equation of tangent of = 1 is
y = mx ±     ...... (ii)
On comparing (i) & (ii)
= ±     ...... (iii)
⇒ a² = 4 ⇒ a = ± 2    ....... (iv)
Using (iii) & (iv) we get m = ±
So equation of other common tangent is
x + 2y + 4 = 0.

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