Find the equation of the tangent to the parabola y²= 16x perpendicular to 2x +2y+3 = 0
pls tell me ans ..i dont know how to solve ... because i am getting prepared for tommorow exam..
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Step-by-step explanation:
Equation of the parabola is y
2
=16x
The tangent is parallel to 2x−y+5=0
Equation of the tangent can be taken as y=2x+c
Condition for tangency is c =
m
a
=
2
4
=2
Equation of the tangent can be taken as y=2x+2
⇒2x−y+2=0
Point of contact is (
m
2
a
,
m
2a
)=(
4
4
,
2
8
)=(1,4)
Slope of the perpendicular tangent is m
′
=−
m
1
=
2
−1
Equation of the perpendicular tangent is y=m
′
x+c
′
=(−
2
1
)x+c
′
where c
′
=
m
′
a
=(
(−
2
1
)
4
)=−8
Equation of the perpendicular tangent is y=−
2
1
x−8⇒2y=−x+16⇒x+2y+16=0
Point of contact is (
(
4
1
)
4
,
(−
2
1
)
8
)=(16,−16)
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