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Question
Find the equation of the following parabolas:
Vertex at (0, 4), focus at (0, 2)
Solution
Given that vertex at (0, 4) and focus at (0, 2).
So, the equation of directrix is y – 6 = 0
According to the definition of the parabola
PF = PM.
`sqrt((x - 0)^2 + (y - 2)^2) = |y - 6|`
⇒ `sqrt(x^2 + y^2 + 4 - 4y) = |y - 6|`
Squaring both the sides, we get
x2 + y2 + 4 – 4y = y2 + 36 – 12y
⇒ x2 + 4 – 4y = 36 – 12y
⇒ x2 + 8y – 32 = 0
⇒ x2 = 32 – 8y
Hence, the required equation is x2 = 32 – 8y.
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