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Home Q & A Board Science-Related Homework Help Mathematics
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michellexox michellexox
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11 years ago
A variable parabola is drawn touching the x-axis at origin and having its vertex on the line y = 2. Prove that axis of this parabola is tangential to a fixed parabola.
Could you explain?I couldn't understand how you arrived at the equation of the variable parabola and the next steps as well.
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#1
11 years ago
the variable parabola is:

y - 2 = -k(x - a)^2

y = -kx^2 + 2ka x - ka^2 + 2

then
ka^2 = 2
k = (2/a^2)

thus
y - 2 = (-2/a^2) (x - a)^2

the axis is x = a.

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