A tangent line is drawn to the hyperbola xy = c at a point P. (a) Show
Question:
A tangent line is drawn to the hyperbola xy = c at a point P.
(a) Show that the midpoint of the line segment cut from this tangent line by the coordinate axes is P.
(b) Show that the triangle formed by the tangent line and the coordinate axes always has the same area, no matter where P is located on the hyperbola.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 71% (7 reviews)
a The slope of the tangent line at Its equation is so its yintercept is ...View the full answer
Answered By
Fahmin Arakkal
Tutoring and Contributing expert question and answers to teachers and students.
Primarily oversees the Heat and Mass Transfer contents presented on websites and blogs.
Responsible for Creating, Editing, Updating all contents related Chemical Engineering in
latex language
4.40+
8+ Reviews
22+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
Let (x1, y1) be the coordinates of a point on the parabola x2 = 4py. The equation of the line that just touches the parabola at the point (x1, y1), called a tangent line, is y y1 = x1 / 2p (x x1)....
-
A line perpendicular to another line or to a tangent line is called a normal line. Find an equation of the line perpendicular to the line that is tangent to the following curves at the given point P....
-
A line perpendicular to another line or to a tangent line is called a normal line. Find an equation of the line perpendicular to the line that is tangent to the following curves at the given point P....
-
A wooden bookshelf has external dimensions as follows :Height = 110cm, Depth = 25cm, Breadth = 85cm (see figure). The thickness of the plank is 5 cm everywhere. The external faces are to be polished...
-
Refer to the Cold Springs Filtration Department Data Set. 1. Compute the November conversion costs in the Filtration Department. 2. If the Filtration Department completely processed 225,000 liters,...
-
Miss Muffet always likes to have things just so. In fact the only way she will consume her curds and whey is in the ratio of 2 units of whey per unit of curds. She has an income of $20. Whey costs...
-
Show that the normal functions corresponding to the longitudinal vibration of the bar shown in Fig. 8.29 are orthogonal. x=0 1000 k x=/ FIGURE 8.29 Bar fixed at one end and connected to a spring at...
-
The condensed income statement for the Consumer Products Division of Milner Industries Inc. is as follows (assuming no service department charges): Sales ...............$ 7,000,000 Cost of goods sold...
-
Inventory, by Product Category Quantity Per Unit Cost Net Realizable Value Tools: Hammers Saws Screwdrivers Paint products: 1-gallon cans Paint brushes 110 $ 5.40 $5.90 240 10.40 9.40 340 2.40 3.00...
-
Yakima Wheat Company acquired harvesting equipment for $90,000 with an expected useful life of 5 years and a $10,000 expected residual value. Yakima Wheat used straight-line depreciation. During its...
-
(a) Graph the function (b) By calculating values of f (x), give numerical estimates of the limits in part (a). (c) Calculate the exact values of the limits in part (a). Did you get the same value or...
-
Evaluate 1000 - 1 lim 1 >1
-
Show that 1000 L of home heating oil with energy density of about 40 MJ/L are required to provide heat for our typical dwelling (A H = 100 m 2 , C H = 10 MJ/K,R H = 0.7 m 2 K/W) in Boston. Assume...
-
Akeem Joffer hopes to a new cabin on Webb Lake in Maine. Akeem has $ 1 3 , 0 0 0 saved today and wants to save $ 7 , 0 0 0 every year for the next nine years. Assume Akeem can earn 1 1 % on his...
-
On the 1 January 2 0 1 8 , Easy Stone Limited, acquired the popular brand, Just Brick It for an amount of R 3 5 0 0 0 0 0 which was paid in full on this date. Legal fees of R 1 5 0 0 0 0 was spent in...
-
july 1 st k . samuels, sole shareholder of samuels internet cafe ltd , started his business by investing by investing his cash saving of $ 8 2 0 0 for 1 0 0 shares of the business . 1 st , Recevied a...
-
The Pet Paradise Pet Shop, specialized in selling pet houses, is currently facing profitability challenges. The founder, Lisa, recognizes your expertise in business knowledge and financial acumen and...
-
Use the following information to answer the next question. While performing a titration between CH3COOH(aq) and CSOH(aq), a student made the following observations (i) Methyl red is a good indicator...
-
Describe the steps you took to identify one of the dinosaurs from the fossil?
-
F.(3e* -2x 3 sin(2x)) is equal to 2 3 Cos 8. IT 3, t (4+@ 2 3, 1+o 1 4 Cos 4 4 1 3. 1 +4cos V7 (1+o 4 1 4 Cos 4 1+0 4-
-
Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis. (a) y = x4, y = 0, x = 1; about x = 2 (b) y = 4x - x2, y...
-
Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis. (a) y = x4, y = 0, x = 1; about x = 2 (b) y = 4x - x2, y...
-
(1) Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curve about the specified axis. (2) Use your calculator to evaluate the integral correct to...
-
Drilling Company uses activity-based costing and provides this information: Driver Rate Manufacturing Activity Cost Driver Materials handling Number of parts $ 0.60 Machinery Number of machine hours...
-
You are hoping to implement a project to distribute free fertilizer to farmers. In the current year (year 0), there will be an upfront administrative cost of $200 of setting up the program. Then,...
-
A owns ABC, Inc., an S corporation. A's stock basis was $10,000 at the beginning of year 1 and he loaned ABC $3,000 on Jan. 1. ABC has loss of $15,000 for the year. 30. How much of the loss can A...
Study smarter with the SolutionInn App