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Chapter 10: Q. 57 (page 644)

Write an equation for each parabola.

Short Answer

Expert verified

The equation of the parabola is $y^{2} + 2 y + x - 3 = 0$ .

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

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

03

Step 3. Find the equation of parabola .

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

localid="1646931030050" ${(y - k)}^{2} = - 4 a (x - h) {(0 - 1)}^{2} = - 4 a (1 - 2) a = \frac{1}{4}$

Further simplify .

Substitute the value of a in the equation of parabola .

localid="1646931164241" ${(y - k)}^{2} = - 4 a (x - h) {(y - 1)}^{2} = - 4 \times \frac{1}{4} (x - 2) y^{2} + 2 y + x - 3 = 0$

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Most popular questions from this chapter

If $θ$ is acute, the Half-angle Formula for the cosine function is $\cos \frac{θ}{2} =_______$ .

The standard equation of a circle with center at $(2, - 3)$ and radius 1 is ________.

Find an equation for each ellipse. Graph the equation by hand.

Foci at $(5, 1)$ and $(- 1, 1)$ : length of the major axis is $8$ .

Use the Square Root Method to find the real solutions of ${(x + 4)}^{2} = 9$ .

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.

localid="1647365908255" $x^{2} + 4 x y + y^{2} - 3 = 0$

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