The length of latus rectum of the parabola 4y² = 14x is
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Step-by-step explanation:
4y
2
+3x+3y+1=0
⇒4y
2
+3y=−3x−1 ,take 3x+1 to RHS
⇒y
2
+
4
3
y=−
4
3
x−
4
1
,divide each sides by 4
⇒y
2
+2⋅
8
3
y+(
8
3
)
2
=−
4
3
x−
4
1
+(
8
3
)
2
,add each sides (
8
3
)
2
⇒(y+
8
3
)
2
=−
4
3
x−
4
1
+
64
9
=−
4
3
x−
64
15
⇒(y+
8
3
)
2
=−
4
3
(x+
16
5
)
Now comparing above equation with standard parabola Y
2
=−4aX
Length of latus rectum =4a=
4
3
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