Conics Parabolas

By Garreth Carpenter

What is the equation of the directrix of the parabola whose equation is​

y2 = 10x​

By Garreth Carpenter

​•Converting y2 = 10x to y2 = 4ax form

• we get 4ax = 10x ⇒ a = 2.5 So the focus is at (2.5, 0)

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The directrix is on the opposite side of the origin to the focus, so the directrix of y2 = 10x is x = -2.5

By Garreth Carpenter

​What is the equation of the directrix of the parabola whose equation is

​x2 = -25y

​•Converting x2 = -25y to x2 = 4ay form

•we get:

​•⇒ 4ay = -25y ⇒ a = -6.25 The directrix is on the opposite side of the origin to the focus (0, -6.25) So the directrix of x2 = -25y is the line y = 6.25

By Garreth Carpenter

​Where is the focus of the parabola whose equation is

​y2 + 32x = 0

​•y2 + 32x = 0 ⇒ y2 = -32x Converting y2 = -32x to y2 = 4ax form

• we get ⇒ 4ax = -32x ⇒ a = -8 So the focus of y2 + 32x = 0 is F = (-8,0)

​x2 - 9y = 0

•x2 - 9y = 0 ⇒ x2 = 9y

•Converting x2 = 9y to x2 = 4ay form, we get ⇒ 4ay = 9y ⇒ a = 9/4 = 2.25 So the focus of x2 - 9y = 0 is F = (0, 2.25)

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y2 + 12x = 0

•y2 + 12x = 0 ⇒ y2 = -12x

•Converting y2 = -12x to y2 = 4ax form

•we get 4ax = -12x ⇒ a = -3 The directrix is on the opposite side of the origin to the focus (-3, 0) So the directrix of y2 = -12x is the line x = 3

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x2 - 30y = 0

•x2 - 30y = 0 ⇒ x2 = 30y

• Converting x2 = 30y to x2 = 4ay form, we get: ⇒ 4ay = 30y  ⇒ a = 7.5 The directrix is on the opposite side of the origin to the focus (0, 7.5) So the directrix of x2 = 30y is the line y = -7.5

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