Find the equation of the parabolar whose vertex is the origin and whose focus is the point F(4,0)
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Answer:
From the given detail is clear that the parabola is open downwards.
Hence the equation is of the form(x−h)
2
=−4a(y−k)
Given vertex V is (0,4) and focus (0,2).
The distance between the vertex and the focus is VF=a
VF=
(0−0)
2
+(2−4)
2
=2
Hence a=2
∴The required equation of the parabola is (x−0)
2
=−4(2)(y−4)
x
2
=−8(y−4) = x
2
=32−8y is the required equation of the parabola.
Step-by-step explanation:
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