If y = 2 x + c is tangent to parabola y 2 = 8 x .Then find the value of c .
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Equation of tangent on point
(
x
1
,
y
1
)
on parabola is
y
y
1
=
4
(
x
+
x
1
)
.
On comparing above equation with given equation of tangent ,
y
=
2
x
+
c
,
⇒
y
1
=
2
and
x
1
=
c
/
2
.
Point
(
x
1
,
y
1
)
lies on given parabola,
4
=
8
(
2
c
)
⇒
c
=
1
Simple standard approach.
Its not a 10sec approach!
how to do it in 10 sec ? it took 16 sec. lol !
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Tangent of slope m to parabola y 2 = 4 ( 2 ) x is y = m x + m 2 . Tangent of slope 2 will be : y = 2 x + 1 ⟹ c = 1