Hi there. Bit of a headscratcher here. I am perplexed by part (c) of the attached question.
I understand that if the tangent makes an angle of pi/4 with the horizontal axis, this is equal to a gradient of 1. When I plug this into the value of dy/dx I worked out, I come out with the same coordinates as those in part b) ! This surely can't be.
my answer to part a) : dy/dx = (2x  y) / (x + 1  2y)
part b) stationary when 2x  y = 0, therefore sub y = 2x into first equation, and you come out with a quadratic 3x^2  2x 1 = 0 and this solves for x is 1/3 or + 1
then c) as dy/dx is equal to 1, then 2x  y = x + 1  2y
this rearranges to y = 1 x however when you sub that in you get the same quadratic as b) , please help!
I understand that if the tangent makes an angle of pi/4 with the horizontal axis, this is equal to a gradient of 1. When I plug this into the value of dy/dx I worked out, I come out with the same coordinates as those in part b) ! This surely can't be.
my answer to part a) : dy/dx = (2x  y) / (x + 1  2y)
part b) stationary when 2x  y = 0, therefore sub y = 2x into first equation, and you come out with a quadratic 3x^2  2x 1 = 0 and this solves for x is 1/3 or + 1
then c) as dy/dx is equal to 1, then 2x  y = x + 1  2y
this rearranges to y = 1 x however when you sub that in you get the same quadratic as b) , please help!
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