14. The curve with implicit equation x² + y² - 2x + 2y = 23 is given. a. Show that there are two points on the curve for which the y-coordinate equals 2. b. Find the equations of the tangent lines to the curve at both of these points. Find the intersection of these tangents. (Use implicit differentiation!) c. In which point (s) of the curve is the tangent parallel to the straight line with equation 3x+4y = 0?
14. The curve with implicit equation x² + y² - 2x + 2y = 23 is given. a. Show that there are two points on the curve for which the y-coordinate equals 2. b. Find the equations of the tangent lines to the curve at both of these points. Find the intersection of these tangents. (Use implicit differentiation!) c. In which point (s) of the curve is the tangent parallel to the straight line with equation 3x+4y = 0?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.4: Definition Of The Derivative
Problem 1YT: YOUR TURN For the graph of f(x)=x2x, a find the equation of the secant line through the points where...
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![14. The curve with implicit equation x² + y² - 2x + 2y = 23 is given.
a. Show that there are two points on the curve for which the y-coordinate equals 2.
b. Find the equations of the tangent lines to the curve at both of these points. Find the intersection
of these tangents. (Use implicit differentiation!)
c. In which point (s) of the curve is the tangent parallel to the straight line with equation 3x+4y=0?
d. In which point(s) of the curve is the tangent parallel tot the y-axis?
e. What kind of curve corresponds to the equation? Check all the answers to the previous questions
on an accurate drawing.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf39e9cd-272b-46eb-bc9a-119687829646%2Fd76b48d5-6b38-4c77-ae3b-7140a7bde899%2F1hkimp_processed.png&w=3840&q=75)
Transcribed Image Text:14. The curve with implicit equation x² + y² - 2x + 2y = 23 is given.
a. Show that there are two points on the curve for which the y-coordinate equals 2.
b. Find the equations of the tangent lines to the curve at both of these points. Find the intersection
of these tangents. (Use implicit differentiation!)
c. In which point (s) of the curve is the tangent parallel to the straight line with equation 3x+4y=0?
d. In which point(s) of the curve is the tangent parallel tot the y-axis?
e. What kind of curve corresponds to the equation? Check all the answers to the previous questions
on an accurate drawing.
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