Show that the tangent line at a point P (x0, y0) on the hyperbola (x a) 2 (y b) 2 1 has equation Ax By 1 where A a and B Yo 62...

The equation of the tangent line is y yo m xxo m Sub ...

Show that the tangent line at a point P = (x0, y0) on the hyperbola (x/a) 2

Question:

Show that the tangent line at a point P = (x0, y0) on the hyperbola (x/a)²−(y/b)²= 1 has equation Ax − By = 1 where A = a and B Yo 62

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

See More Books

Question Posted: Dec 25, 2023 08:29 AM

See More Questions

Prove that the tangent line at a point P on the cycloid always passes through the top point on the rolling circle as indicated in Figure 22. Assume the generating circle of the cycloid has radius 1....
Points R 1 and R 2 in Figure 25 are defined so that F 1 R 1 and F 2 R 2 are perpendicular to the tangent line. (a) Show, with A and B as in Exercise 70, that (b) Use (a) and the distance formula to...
Descartess method for finding tangents depends on the idea that, for many graphs, the tangent line at a given point is the unique line that intersects the graph at that point only. Apply his method...
The following table includes transactions carried out by Ram Horn Corporation, as well as columns for each of the three categories found in the statement of cash flows: operating, financing, and...
The following transactions were completed by The Bronze Gallery during the current fiscal year ended December 31: June 6. Reinstated the account of Ian Netti, which had been written off in the...
Determine the coordinates of the focus and the equation of the directrix of the given parabolas. Sketch each curve. x 2 = 4y
Is the coefficient of restitution $e$ different in two inertial reference frames, which are moving at constant velocity relative to each other? (See Eq. 5.18 if you have forgotten the definition of...
The following transactions occurred in January at Tarnsdale Fabricators, a manufacturer of custom tools: 1. Purchased $17,000 of materials. 2. Issued $16,800 in direct materials to the production...
The Reading Warehouse distributes hardback books to retail stores and extends credit terms of 2/7, n/30 to all of its customers. During the month of June the following inventory transactions...
Broncos Corp. manufactures wooden frames with the bronco medallion for framing the college degrees awarded by Western Michigan University. Each Bronco frame sells for $150 and requires: 5 linear...
Find the equation of the ellipse consisting of points P such that PF 1 + PF 2 = 12, where F 1 = (4, 0) and F 2 = (2, 0).
Show that the eccentricity of a hyperbola in standard position is e = 1 + m 2 , where m are the slopes of the asymptotes.
The following statistics and estimates were compiled by Big Moon Bank regarding a proposed new branch office and the bank itself: Branch office expected return ............ = 15% Standard deviation...
What is the major difference between a cross-sectional and a longitudinal design?
Define a sampling strategy.
Describe some of the threats to external validity that are common with the survey approach.
Define the two major types of sampling strategies .
What type of scenario would warrant the application of a longitudinal design overall a cross-sectional design?
On January 1, 2008, you win $40,000,000 in the state lottery. The $40,000,000 prize will be paid in equal installments of $2,000,000 over 20 years. The payments will be made on December 31 of each...
1-Stern observed all of the following results EXCEPT _______ in his experiment. A-one of the recombinant phenotypes was associated with an X chromosome of normal length B-the number of car, B+ male...
a. Find the critical points of f on the given interval. b. Determine the absolute extreme values of f on the given interval when they exist. c. Use a graphing utility to confirm your conclusions....
Let f(x) = c, where c is a positive constant. Explain why an area function of f is an increasing function.
Explain how Riemann sum approximations to the area of a region under a curve change as the number of subintervals increases.
Use the generic graph I h(x) 3 A 6 B 5 B 4 1 5 C 2 3 D 2 E 1 F F 0 34 search method covered in class, carry out BFS, DFS, uniform-cost, and A* over the graph and the heuristic function given in the...
a. Find the equivalent resistance of the circuit shown. The voltage of the battery is 110 V, and the resistances are as follows: R = 402; R2 = 60; R3 = 12 Q; R4 = 17 Q; R5 = 42 Q; R6 = 12 Q; R7 = 10...
Two point charges of 61.4 C and 17.4 C exert a force of repulsion of 3 N on each other? Determine separation distance between the two charges.

Show that the tangent line at a point P = (x0, y0) on the hyperbola (x/a) 2

Question:

where A = Хо a² and B Yo 62

Step by Step Answer:

The equation of the tangent line is y yo m xxo m Sub...View the full answer

Calculus

Students also viewed these Mathematics questions