Explanation Given: The given equation of the ellipse is, x 2 − 4 x + 9 y 2 + 54 y + 76 = 0 Approach: The standard equation of ellipse whose center is not at origin is, A ( x − h ) 2 + B ( y − k ) 2 = C Here, A , B and C are nonzero real numbers and center is at ( h , k ) . The formula to calculate the distance of a line segment with the given endpoints ( x 1 , y 1 ) and ( x 2 , y 2 ) is, d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 Here, d is the length of the line segment. Calculation: Consider the given equation of ellipse. x 2 − 4 x + 9 y 2 + 54 y + 76 = 0 Express the above equation in the standard form by completing the square. x 2 − 4 x + 9 y 2 + 54 y + 76 = 0 ( x 2 − 4 x + 2 2 ) + 9 ( y 2 + 6 y + 3 2 ) = − 76 + 2 2 + 9 ( 3 2 ) ( x 2 − 4 x + 4 ) + 9 ( y 2 + 6 y + 9 ) = − 76 + 4 + 81 ( x − 2 ) 2 + 9 ( y + 3 ) 2 = 9 ... ( 1 ) Compare the equation ( 1 ) with the standard equation A ( x − h ) 2 + B ( y − k ) 2 = C . The value of h is 2 and k is − 3 . Thus, the center of the ellipse is ( h , k ) = ( 2 , − 3 ) . To find the horizontal endpoints, substitute − 3 for y in equation ( 1 ) . ( x − 2 ) 2 + 9 ( ( − 3 ) + 3 ) 2 = 9 ( x − 2 ) 2 = 9 x − 2 = ± 3 x = 2 ± 3 Solve for the two values of x . x = 2 + 3 = 5 And, x = 2 − 3 = − 1 Thus, the end points are ( − 1 , − 3 ) and ( 5 , − 3 ) . To find the vertical endpoints, substitute 2 for x in equation ( 1 )

10th Edition

ISBN: 9781305191495

Author: Jerome E. Kaufmann; Karen L. Schwitters

Publisher: Cengage Learning US

See similar textbooks

Concept explainers

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is…

Videos

Question

Chapter 8.CR, Problem 21CR

To determine

To find:

The length of the major axis and the length of the minor axis for the ellipse of given equation.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.CR, Problem 20CR

Chapter 8.CR, Problem 22CR

Students have asked these similar questions

Q1: A: Let M and N be two subspace of finite dimension linear space X, show that if M = N then dim M = dim N but the converse need not to be true. B: Let A and B two balanced subsets of a linear space X, show that whether An B and AUB are balanced sets or nor. Q2: Answer only two A:Let M be a subset of a linear space X, show that M is a hyperplane of X iff there exists ƒ€ X'/{0} and a € F such that M = (x = x/f&x) = x}. fe B:Show that every two norms on finite dimension linear space are equivalent C: Let f be a linear function from a normed space X in to a normed space Y, show that continuous at x, E X iff for any sequence (x) in X converge to Xo then the sequence (f(x)) converge to (f(x)) in Y. Q3: A:Let M be a closed subspace of a normed space X, constract a linear space X/M as normed space B: Let A be a finite dimension subspace of a Banach space X, show that A is closed. C: Show that every finite dimension normed space is Banach space.

• Plane II is spanned by the vectors: P12 P2 = 1 • Subspace W is spanned by the vectors: W₁ = -- () · 2 1 W2 = 0

Three streams - Stream A, Stream B, and Stream C - flow into a lake. The flow rates of these streams are not yet known and thus to be found. The combined water inflow from the streams is 300 m³/h. The rate of Stream A is three times the combined rates of Stream B and Stream C. The rate of Stream B is 50 m³/h less than half of the difference between the rates of Stream A and Stream C. Find the flow rates of the three streams by setting up an equation system Ax = b and solving it for x. Provide the values of A and b. Assuming that you get to an upper-triangular matrix U using an elimination matrix E such that U = E A, provide also the components of E.

Chapter 8 Solutions

Intermediate Algebra

Ch. 8.1 - For Problems 110, answer true or false. The graph...Ch. 8.1 - Prob. 2CQ Ch. 8.1 - Prob. 3CQ Ch. 8.1 - Prob. 4CQ Ch. 8.1 - Prob. 5CQ Ch. 8.1 - Prob. 6CQ Ch. 8.1 - Prob. 7CQ Ch. 8.1 - Prob. 8CQ Ch. 8.1 - Prob. 9CQ Ch. 8.1 - Prob. 10CQ

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The length of the major axis and the length of the minor axis for the ellipse of given equation.

Solution Summary: The author calculates the length of the major and minor axis for the ellipse of a given equation by completing the square.

Concept explainers

Videos

To find: The length of the major axis and the length of the minor axis for the ellipse of given equation.

Want to see the full answer?

Chapter 8 Solutions

To find:

The length of the major axis and the length of the minor axis for the ellipse of given equation.