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Chapter 10: Q. 59 (page 644)

Write an equation for each parabola.

Short Answer

Expert verified

The equation of the parabola is $x^{2} = 4 (y - 1)$ .

Step by step solution

01

Step 1. Given information .

Consider the given graph and the points located on it .

02

Step 2. Formula used .

The formula used to find the equation of parabola is ${(x - h)}^{2} = 4 a (y - k)$ .

where h , k are the points of vertex $(h, k) = (0, 1)$ and focus $(x, y) = (2, 2)$ .

03

Step 3. Find the equation of the parabola .

Substitute the value of $(h, k) = (0, 1)$ and $(x, y) = (2, 2)$ in the equation of parabola .

localid="1646929727056" ${(x - h)}^{2} = 4 a (y - k) {(2 - 0)}^{2} = 4 a (2 - 1) a = 1$

Further simplify .

Substitute the value of a in the equation of parabola .

localid="1646930160222" $(x - h^{2}) = 4 a (y - k) {(x - 0)}^{2} = 4 \times 1 (y - 1) x^{2} = 4 (y - 1)$

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Most popular questions from this chapter

Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.

Vertex at $(0, 0)$ ; axis of symmetry is y-axis ; containing the point $(2, 3)$ .

The graph of a parabola is given. Match graph to its equation.

and equations are,

$A) y^{2} = 4 x C) y^{2} = - 4 x E) {(y - 1)}^{2} = 4 (x - 1) G) {(y - 1)}^{2} = - 4 (x - 1) B) x^{2} = 4 y D) x^{2} = - 4 y F) {(x + 1)}^{2} = 4 (y + 1) H) {(x + 1)}^{2} = 4 (y + 1)$

In Problems 31– 42, rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation. Refer to Problems 21–30 for Problems 31– 40. $11 x^{2} + 10 \sqrt{3} x y + y^{2} - 4 = 0$

In Problems 43–52, identify the graph of each equation without applying a rotation of axes.

9 x^{2} + 12 x y + 4 y^{2} - x - y = 0

Semi elliptical Arch Bridge: A bridge is built in the shape of a semi elliptical arch. The bridge has a span of $120$ feet and a

maximum height of $25$ feet. Choose a suitable rectangular coordinate system and find the height of the arch at distances

of $10, 30$ and $50$ feet from the center.

See all solutions

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