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Chapter 10: Q. 56 (page 644)

Write an equation for the parabola.

Short Answer

Expert verified

The equation of the parabola is $x^{2} - 2 x + y - 1 = 0$ .

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 $(h, k) = (1, 2)$ and focus $(x, y) = (2, 1)$ .

03

Step 3. Find the equation of parabola .

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

${(x - h)}^{2} = - 4 a (y - k) {(2 - 1)}^{2} = - 4 a (1 - 2) a = \frac{1}{4}$

Further simplify .

Substitute the value of a in the equation of parabola .

localid="1646931694920" ${(x - h)}^{2} = - 4 a (y - k) {(x - 1)}^{2} = - 4 \times \frac{1}{4} (y - 2) x^{2} - 2 x + y - 1 = 0$

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Most popular questions from this chapter

To complete the square of $x^{2} - 3 x$ , add $______$ .

Graph each function.

$f (x) = \sqrt{9 - 9 x^{2}}$ .

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

10 x^{2} - 12 x y + 4 y^{2} - x - y - 10 = 0

In Problems 31– 42, rotate the axes so that the new equation contains no $x y$ -term. Analyze and graph the new equation. Refer to Problems 21–30 for Problems 31– 40.

5 x^{2} + 6 x y + 5 y^{2} - 8 = 0

See all solutions

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