The equation of a parabola is given, where the focus is (4,0) and the directrix is x-10=0. Using the standard formula for a parabola, y = a(x-h)^2 + k, along with the given focus and directrix, the equation is determined to be y=-(x-4)^2/20 + 25.
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1. Find the equation of parabola whose focus is (4,0) and directrix is x-10=0. (conics)
Solution
The equation of parabola is given by:
y = a(x-h)^2 + k^2
h = 4
k = (10+0)/2
k = 5
a = 1/(2*0 - 2*10)
a = -1/20
y = -(1/20)*(x-4)^2 + 25
The equation of parabola is y=-(x-4)^2/20 + 25.