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1. Find the equations of both the tangent lines to the hyperbola x² - 4y² = 9 that pass through the point (-3,3). Note that the point (-3, 3) is not on the hyperbola.

1. Find the equations of both the tangent lines to the hyperbola x² - 4y² = 9 that pass through the point (-3,3). Note that the point (-3, 3) is not on the hyperbola.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Find the equations of both the tangent lines to the hyperbola x² - 4y² = 9 that pass through the point (-3,3). Note that the point (-3, 3) is not on the hyperbola. 2. a. Find lim sinx csc6x x-0 b. If g(0) = sine, find g". Give exact values. 3. x+1 a. For the function f(x) at which point(s) does the tangent line have a slope of -1? Give exact answers. x-1 b. Find an equation of the tangent line(s) at the point(s) in a. Give exact answers. 4. If a tank holds 50,000 litres of water which drains from the bottom of the tank in 40 minutes, then the volume of water, V, which remains in the tank after t minutes is given by V(t) = 50000 (1-² 0≤t≤ 40 a. Find the rate at which water is draining from the tank after 10 minutes and after 20 minutes. b. At what time is the water flowing the fastest? At which time is it flowing the slowest?
Transcribed Image Text:1. Find the equations of both the tangent lines to the hyperbola x² - 4y² = 9 that pass through the point (-3,3). Note that the point (-3, 3) is not on the hyperbola. 2. a. Find lim sinx csc6x x-0 b. If g(0) = sine, find g". Give exact values. 3. x+1 a. For the function f(x) at which point(s) does the tangent line have a slope of -1? Give exact answers. x-1 b. Find an equation of the tangent line(s) at the point(s) in a. Give exact answers. 4. If a tank holds 50,000 litres of water which drains from the bottom of the tank in 40 minutes, then the volume of water, V, which remains in the tank after t minutes is given by V(t) = 50000 (1-² 0≤t≤ 40 a. Find the rate at which water is draining from the tank after 10 minutes and after 20 minutes. b. At what time is the water flowing the fastest? At which time is it flowing the slowest?
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