Exercise 47 Page 348

Before we begin, note that in the given equation the variable that is raised to the second power is y. y^2=2/5x Therefore, the axis of symmetry of the parabola is a horizontal line.

Finding the Desired Information

x=1/4 p(y- k)^2+ h Let's rearrange the given equation.

y^2=2/5x

MultEqn

LHS * 5/2=RHS* 5/2

5/2y^2=x

RearrangeEqn

Rearrange equation

x=5/2y^2

We need to identify the values of h, k, and p. Let's start with p. To do so, we will solve the equation 14 p= 52. We set it equal to 52 because it is the coefficient of the y^2 term.

1/4p=5/2

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Solve for p

MultEqn

LHS * 2/5=RHS* 2/5

1/4p(2/5)=1

MultFrac

Multiply fractions

2/20p=1

MultEqn

LHS * p=RHS* p

2/20=p

ReduceFrac

a/b=.a /2./.b /2.

1/10=p

RearrangeEqn

Rearrange equation

p=1/10

Knowing that p= 110, we can rewrite the equation. x=5/2y^2 ⇕ x=1/4( 1/10)(y- 0)^2+ 0 Now we have that h= 0, k= 0, and p= 110. By recalling the corresponding formulas, we can find the focus, directrix, and axis of symmetry of the parabola.

	Focus	Directrix	Axis of Symmetry
Formula	( h+ p, k)	x= h- p	y= k
Value	( 0+ 1/10, 0) ⇓ (1/10,0)	x= 0- 1/10 ⇓ x=- 1/10	y= 0

Drawing the Parabola

Now, let's draw the parabola using the obtained information.