CircleMedium
Question
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 -
= 1 (a > √3), then the value of a, k and other common tangent are given by -Options
A.a = 2
B.a = - 2
C.x + 2y + 4 = 0
D.k = 4
Solution
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.
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 isy = 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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