Explanation Given: The equation is x 2 = 16 y . Concept Used: The equation of the parabola having vertex ( h , k ) and directrix y = − c is ( x − h ) 2 = 4 c ( y − k ) . The parabola has vertex ( 0 , 0 ) , vertical axis x = 0 and opens upwards if c > 0 or opens downwards if c < 0 , where the focus ( 0 , c ) is a distance | c | from the vertex. Calculation: Write the given equation x 2 = 16 y in the standard form of parabola ( x − h ) 2 = 4 c ( y − k ) as follows: x 2 = 16 y ( x − 0 ) 2 = 4 ( 4 ) ( y − 0 ) Compare the equation ( x − 0 ) 2 = 4 ( 4 ) ( y − 0 ) with the standard form of the parabola ( x − h ) 2 = 4 c ( y − k ) to obtain the value of c , h and k

7th Edition

ISBN: 9780134696522

Author: HORNSBY, John, Lial, Margaret L., Rockswold, Gary K.

Publisher: Pearson Education, Inc.,

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

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Chapter 8.1, Problem 67E

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To find: The focus, directrix and the axis of parabola x2=16y.

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Chapter 8.1, Problem 66E

Chapter 8.1, Problem 68E

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Simply:(p/(x-a))-(p/(x+a))

Q1lal Let X be an arbitrary infinite set and let r the family of all subsets F of X which do not contain a particular point x, EX and the complements F of all finite subsets F of X show that (X.r) is a topology. bl The nbhd system N(x) at x in a topological space X has the following properties NO- N(x) for any xX N1- If N EN(x) then x€N N2- If NEN(x), NCM then MeN(x) N3- If NEN(x), MEN(x) then NOMEN(x) N4- If N = N(x) then 3M = N(x) such that MCN then MeN(y) for any уем Show that there exist a unique topology τ on X. Q2\a\let (X,r) be the topology space and BST show that ẞ is base for a topology on X iff for any G open set xEG then there exist A Eẞ such that x E ACG. b\Let ẞ is a collection of open sets in X show that is base for a topology on X iff for each xex the collection B, (BEB\xEB) is is a nbhd base at x. - Q31 Choose only two: al Let A be a subspace of a space X show that FCA is closed iff F KOA, K is closed set in X. الرياضيات b\ Let X and Y be two topological space and f:X -…

Q1\ Let X be a topological space and let Int be the interior operation defined on P(X) such that 1₁.Int(X) = X 12. Int (A) CA for each A = P(X) 13. Int (int (A) = Int (A) for each A = P(X) 14. Int (An B) = Int(A) n Int (B) for each A, B = P(X) 15. A is open iff Int (A) = A Show that there exist a unique topology T on X. Q2\ Let X be a topological space and suppose that a nbhd base has been fixed at each x E X and A SCX show that A open iff A contains a basic nbdh of each its point Q3\ Let X be a topological space and and A CX show that A closed set iff every limit point of A is in A. A'S A ACA Q4\ If ẞ is a collection of open sets in X show that ẞ is a base for a topology on X iff for each x E X then ẞx = {BE B|x E B} is a nbhd base at x. Q5\ If A subspace of a topological space X, if x Є A show that V is nbhd of x in A iff V = Un A where U is nbdh of x in X.

Chapter 8 Solutions

Graphical Approach To College Algebra

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Identify the graph,...Ch. 8 - Prob. 10T Ch. 8 - Prob. 11T Ch. 8 - Prob. 12T Ch. 8 - Prob. 13T Ch. 8 - Prob. 14T Ch. 8 - Prob. 15T Ch. 8 - Prob. 16T

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The focus, directrix and the axis of parabola x 2 = 16 y .

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To find: The focus, directrix and the axis of parabola x2=16y.

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Chapter 8 Solutions