ParabolaHard
Question
The equations of the common tangents to the parabola y = x2 and y = - (x - 2)2 is/are
Options
A.y = 4 (x - 1)
B.y = 0
C.y = - 4 (x - 1)
D.y = - 30x - 50
Solution
Equation of tangent to x2 = y is
y = mx -
m2 .....(1)
Equation of tangent to (x - 2)2 = - y is
y = m(x - 2) +m2 .....(2)
(1) and (2) are identical.
⇒ m = 0 or 4
∴ Common tangents are y = 0 and y = 4x - 4.
y = mx -
m2 .....(1)Equation of tangent to (x - 2)2 = - y is
y = m(x - 2) +
m2 .....(2)(1) and (2) are identical.
⇒ m = 0 or 4
∴ Common tangents are y = 0 and y = 4x - 4.
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