Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 15: Problem 1401

The vertex of the parabola \((x-b)^{2}=4 b(y-b)\) is ........ (a) (b,0) (b) \((0, b)\) (c) \((0,0)\) (d) \((\mathrm{b}, \mathrm{b})\)

Short Answer

Expert verified
The vertex of the given parabola \((x-b)^2 = 4b(y-b)\) is (b, b), which corresponds to option (d).

Step by step solution

01

Identify the vertex form of the given parabolic equation

We have the given equation of the parabola as \((x-b)^2 = 4b(y-b)\). Comparing it with the standard vertex form of a parabola, \((x-h)^2 = 4a(y-k)\), we can match the corresponding values.
02

Compare the given equation to the vertex form equation

We have: \((x-b)^2 = 4b(y-b)\) \((x-h)^2 = 4a(y-k)\) Comparing the two equations, we get: h = b k = b a = b Thus, the vertex of the parabola is at the point (h, k) which is (b, b).
03

Determine the correct answer

According to our finding, the vertex of the given parabola is (b, b). Comparing this with the given options, we see that the vertex of the parabola is the point (b, b) which corresponds to option (d). Therefore, the correct answer is (d) \((b, b)\).

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!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The equation \(\left[x^{2} /(1-r)\right]-\left[y^{2} /(1+r)\right]=1 ; r>1\) represents. (a) a parabola (b) an ellipse (c) a circle (d) None of these

The line \(\mathrm{y}=\mathrm{mx}+1\) is a tangent to the parabola \(\mathrm{y}^{2}=4 \mathrm{x}\) if \(\mathrm{m}=\ldots \ldots \ldots \ldots\) (a) 4 (b) 3 (c) 2 (d) 1

If the line \(\mathrm{y}=1-\mathrm{x}\) touches the curve \(\mathrm{y}^{2}-\mathrm{y}+\mathrm{x}=0\), then the point of contact is (a) \((0,1)\) (b) \((1,0)\) (c) \((1,1)\) (d) \([(1 / 2),(1 / 2)]\)

If \(\mathrm{e}_{1}\) and \(\mathrm{e}_{2}\) be the eccentricities of a hyperbola and its conjugate, then \(\left(1 / \mathrm{e}_{1}^{2}\right)+\left(1 / \mathrm{e}_{2}^{2}\right)=\ldots \ldots \ldots\) (a) 2 (b) 1 (c) 0 (d) 3

If PN is the perpendicular from a point on a rectangular hyperbola to its asymptotes, the locus, of the midpoint of PN is (a) A circle (b) a hyperbola (c) a parabola (d) An ellipse
See all solutions

Recommended explanations on English Textbooks

Sociolinguistics

Read Explanation

Essay Writing Skills

Read Explanation

Synthesis Essay

Read Explanation

Phonology

Read Explanation

English Language Study

Read Explanation

International English

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free