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Chapter 10: Q. 4 (page 698)

In Problems 1鈥�10, identify each equation. If it is a parabola, give its vertex, focus, and directrix; if it is an ellipse, give its center, vertices, and foci; if it is a hyperbola, give its center, vertices, foci, and asymptotes

x2+4y=4

Short Answer

Expert verified

The given equation represents a parabola with vertex as(0,1), focus as(1,0)and directrix asy=2

Step by step solution

01

Step 1. Given Information

An equation is given as x2+4y=4

We can rewrite the equation as

x2+4y-4y=4-4yx2=4-4yx2=4(1-y)

02

Step 2. Finding the vertex, foci and directrix

The equation x2=4(1-y)is comparable to (x-h)2=-4a(y-k)which is the equation of a parabola.

The focus of the parabola is(h,k-a)=(1,1-1)=(1,0)

The vertex of the parabola(h,k)=(0,1)

The directrix of the parabola

y=k+ay=1+1y=2

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