Chapter 10: Q 12. (page 643)

The graph of a parabola is given. Match graph to its equation.
and equations are,
$A) y^{2} = 4 x C) y^{2} = - 4 x E) {(y - 1)}^{2} = 4 (x - 1) G) {(y - 1)}^{2} = - 4 (x - 1) B) x^{2} = 4 y D) x^{2} = - 4 y F) {(x + 1)}^{2} = 4 (y + 1) H) {(x + 1)}^{2} = 4 (y + 1)$

Short Answer

Expert verified

The correct match is (G).

Step by step solution

Step 1. Given information.

We have given graph is,

And equations of the parabola are

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

Step 2. Concept used.

Standard equation of the parabola is,

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

Where (h, k) is the vertex of the parabola.

Step 3. Explanation.

We have given graph is,

This parabola is opens to the left and vertex of the parabola is, (1, 1).

Substituting it in to the standard formula of the hyperbola we will get,

${(y - 1)}^{2} = 4 a (x - 1)$

Using the point (0, 3),

${(3 - 1)}^{2} = 4 a (0 - 1) \Rightarrow 4 = - 4 a \Rightarrow a = - 1$

Therefore equation of the parabola is,

${(y - 1)}^{2} = - 4 (x - 1)$

Step 4. Conclusion.

Hence, equation of the parabola for the graph

is ${(y - 1)}^{2} = - 4 (x - 1)$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

The graph of a parabola is given. Match graph to its equation.
and equations are,
$A) y^{2} = 4 x C) y^{2} = - 4 x E) {(y - 1)}^{2} = 4 (x - 1) G) {(y - 1)}^{2} = - 4 (x - 1) B) x^{2} = 4 y D) x^{2} = - 4 y F) {(x + 1)}^{2} = 4 (y + 1) H) {(x + 1)}^{2} = 4 (y + 1)$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept used.

Step 3. Explanation.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Geometry

Mechanics Maths

Decision Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

The graph of a parabola is given. Match graph to its equation.and equations are,A)y2=4xC)y2=-4xE)(y-1)2=4(x-1)G)(y-1)2=-4(x-1)B)x2=4yD)x2=-4yF)(x+1)2=4(y+1)H)(x+1)2=4(y+1)

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept used.

Step 3. Explanation.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Geometry

Mechanics Maths

Decision Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

The graph of a parabola is given. Match graph to its equation.
and equations are,
$A) y^{2} = 4 x C) y^{2} = - 4 x E) {(y - 1)}^{2} = 4 (x - 1) G) {(y - 1)}^{2} = - 4 (x - 1) B) x^{2} = 4 y D) x^{2} = - 4 y F) {(x + 1)}^{2} = 4 (y + 1) H) {(x + 1)}^{2} = 4 (y + 1)$