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Which equation represents a parabola that has a vertex at (4,-5) and aDirectrix at -9y = -0.06(x + 4)2 + 5y = 0.06(x - 4)2 -5y = 0.06(x + 4)2 + 5y = -0.06(x-4)2 - 5



Answer :

Parabola equation , characteristic points

Vertex is the point of minimum-max value

A Directrix is a line outside parabola

Vertex is at (x,y) = (4,-5)

Parabola equation in general is

(x-h)^2 = 4•c•(y-k)

here c = -9

and (h,k) = (4,-5)

Then

(x-4)^2 = 4•(-9) •(y+5) = (-36)•(y+5)

(x-4)^2 = (-36)•(y+5)

Now divide by (-36)

-0.06((x-4)^2 = y + 5

-0.06(x-4)^2 - 5 = y

Looking at options, right answer comes to be D) , last option

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