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Find the points on the curve xy+4=0 at which the tangents are inclined aft an angle of 45°with the x-axis. ?

Find the points on the curve xy+4=0 at which the tangents are inclined aft an angle of 45°with the x-axis. ?

Grade:12

1 Answers

Ujjwal Sharma
35 Points
6 years ago
xy=-4..................................(1)
differentiate this function(using product rule):-
x(dy/dx)+y=0  ===>dy/dx=-y/x
as angle here is 45 so dy/dx=1
this be satisfied at poiny (x1,y1), we will have
y1=-x1.
x1,y1 also satisfies xy=-4. put this in equation of curve
x1(-x1)=-4 ====>x12=4
x1=+2/-2
put value of x in equation (1) to get the values of y
-----------------------------------------------------------------------------------------------------------------------------------
x1=2 ========> y1=-2
(2,-2) 
------------------------------------------------------------------------------------------------------------------------------------
x1=-2 =======>y1=2
(-2,2)
 

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