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Consider the equation 1/4(x – 5) = (y – 2)^2. What is the equation of the directrix?
A.) x = 4.0000
B.) x = 4.7500
C.) x = 4.6250
D.) x = 4.9375

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Answer:

D

Step-by-step explanation:

Find the vertex

¼(x-5) = (y-2)²

x-5 = 4(y-2)²

x = 4(y-2)² + 5

This is a right-opening parabola with vertex (5,2).

focal length p = 1/(4·coefficient of y²) = 0.0625

directrix: x = 5-p = 4.9375

D

The equation of directrix of the parabola will be x = 4, i.e. Option A.

What is directrix ?

Directrix is a straight line distance to which from any point of a conic section is in fixed ratio to the distance from the same point to a focus. The directrix is perpendicular to the axis of symmetry and does not touch the parabola.

We have,

[tex]\frac{1}{4} (x - 5) = (y - 2)^2[/tex]

Now,

Rewrite as,

[tex](x - 5) = 4(y - 2)^2[/tex]

Now,

[tex]x= 4(y - 2)^2+5[/tex]

Now,

Comparing it with the vertex form,

i.e.

[tex]x = a ( y - h )^ 2 + k[/tex]

Vertex of parabola = (2, 5),

So,

Focus at (a, 0),

So,

Focus of the parabola = (4, 0),

i.e., a = 4

Now,

The Equation of directrix is given by x = a

So,

The equation of the directrix of this parabola,

x - a = 0,

i.e.

x - 4 = 0

⇒

x = 4

Hence, we can say that the equation of directrix of the parabola will be x = 4, i.e. Option A.

To know more about directrix click here

https://brainly.com/question/4333610

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