The equation of a closed curve is (x+2y)² +3(x-y) = 27. (i) Show, by differentiation, that the gradient at the point (x, y) on the curve may be dy y-4x expressed in the form dx 7y-x (ii) Find the equations of the tangents to the curve that are parallel to (a) the x-axis, (b) the y-axis. [(ii)(a) y= +2 (b) x=±/7
The equation of a closed curve is (x+2y)² +3(x-y) = 27. (i) Show, by differentiation, that the gradient at the point (x, y) on the curve may be dy y-4x expressed in the form dx 7y-x (ii) Find the equations of the tangents to the curve that are parallel to (a) the x-axis, (b) the y-axis. [(ii)(a) y= +2 (b) x=±/7
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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![The equation of a closed curve is (x+2y)² +3(x-y)² = 27.
(i) Show, by differentiation, that the gradient at the point (x, y) on the curve may be
dy y-4x
expressed in the form
dx 7y-x
(ii) Find the equations of the tangents to the curve that are parallel to
(a) the x-axis, (b) the y-axis.
[(ii)(a) y=±2 (b) x=±/7]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc5ed2325-b942-43b1-ab71-7c85984338db%2F446d1a38-efca-4e21-8406-1a75ff215c4f%2Fsmhrh4d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The equation of a closed curve is (x+2y)² +3(x-y)² = 27.
(i) Show, by differentiation, that the gradient at the point (x, y) on the curve may be
dy y-4x
expressed in the form
dx 7y-x
(ii) Find the equations of the tangents to the curve that are parallel to
(a) the x-axis, (b) the y-axis.
[(ii)(a) y=±2 (b) x=±/7]
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