JEE Main | 2014Dynamics and StatisticsHard
Question
The slope of the line touching both the parabolas y2 = 4x and x2 = - 32y is
Options
A.
B.
C.
D.
Solution
y2 = 4x .....(1)
x2 = -32y ....(2)
m be slope of common tangent Equation of tangent (1)
y = mx +
.........(i)
Equation of tangent (2)
y = mx + 8m2 …(ii)
(i) and (ii) are identical
= 8m2
⇒ m3 =
Alternative method :
Let tangent to y2 = 4x be
y = mx +
as this is also tangent to x2 = - 32y
Solving x2 + 32mx +
= 0
Since roots are equal
∴ D = 0
⇒ (32)2 - 4 ×
= 0
⇒ m3 =
⇒ m =
x2 = -32y ....(2)
m be slope of common tangent Equation of tangent (1)
y = mx +
.........(i)Equation of tangent (2)
y = mx + 8m2 …(ii)
(i) and (ii) are identical
= 8m2⇒ m3 =
Alternative method :
Let tangent to y2 = 4x be
y = mx +
as this is also tangent to x2 = - 32y
Solving x2 + 32mx +
= 0Since roots are equal
∴ D = 0
⇒ (32)2 - 4 ×
= 0⇒ m3 =
⇒ m =
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