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2. The equation x – xy + y? = 3 represents a "rotated ellipse", that is an ellipse whose axes are not parallel to the coordinate axes. (a) Find the points at which this ellipse crosses the x - tangent lines at these points are parallel (b) Where does the perpendicular line to this ellipse at the point (-1,1) intersect the ellipse a second time? axis and show that the

2. The equation x – xy + y? = 3 represents a "rotated ellipse", that is an ellipse whose axes are not parallel to the coordinate axes. (a) Find the points at which this ellipse crosses the x - tangent lines at these points are parallel (b) Where does the perpendicular line to this ellipse at the point (-1,1) intersect the ellipse a second time? axis and show that the

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.1: The Rectangular Coordinate System
Problem 43E: By definition, an ellipse is the locus of points whose sum of distances from two fixed points F1 and...
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2. The equation x2 – xy + y² = 3 represents a “rotated ellipse", that is an ellipse whose axes are not parallel to the coordinate axes. axis and show that the (a) Find the points at which this ellipse crosses the x- tangent lines at these points are parallel (b) Where does the perpendicular line to this ellipse at the point (-1,1) intersect the ellipse a second time? 3. (a) Create a function, f(x) that uses the chain rule and the product rule when finding f'(x). Your function should include a trigonometric function. (b) Find the derivative of the function you found in (a) 4. Let y = 5-2x be the tangent line to a function y = f(x) at x = 3 and y = 2+3x is the tangent line to a function y = g(x) + x at x = line to the function y = h(x) at x = 3? Where h(x) = f(x)g(x) + x2 = 3. What is the tangent 5. (a) Find the points on the graph y? = x³ - 3x + 1 where the tangent line is | horizontal. (b) The tangent line to the graph of y2 +2xy- y = x³ – 2x2 + 2x at the point (0, 1) crosses the graph at one other point. Find it analytically.
Transcribed Image Text:2. The equation x2 – xy + y² = 3 represents a “rotated ellipse", that is an ellipse whose axes are not parallel to the coordinate axes. axis and show that the (a) Find the points at which this ellipse crosses the x- tangent lines at these points are parallel (b) Where does the perpendicular line to this ellipse at the point (-1,1) intersect the ellipse a second time? 3. (a) Create a function, f(x) that uses the chain rule and the product rule when finding f'(x). Your function should include a trigonometric function. (b) Find the derivative of the function you found in (a) 4. Let y = 5-2x be the tangent line to a function y = f(x) at x = 3 and y = 2+3x is the tangent line to a function y = g(x) + x at x = line to the function y = h(x) at x = 3? Where h(x) = f(x)g(x) + x2 = 3. What is the tangent 5. (a) Find the points on the graph y? = x³ - 3x + 1 where the tangent line is | horizontal. (b) The tangent line to the graph of y2 +2xy- y = x³ – 2x2 + 2x at the point (0, 1) crosses the graph at one other point. Find it analytically.
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