Question

angle between the curves x^2 y=4,y(x^2 +4)=8​

Answer 1

Answer:

First solve the equations xy= 4( a rectangular hyperbola) and x2+y2=8 (a circle). Put y= 4x in the 2nd equation. Now, x2+16x2=8 . From here you get two set of solutions x =y=2 and x=y=-2 . These 2 equations intersects at two points (2,2) and (-2,-2). (-2,-2) lies in 3rd quadrant. Now find dydx for both equations at the point (-2,-2). For the 1st one, xdydx+y=0 so, (let) s1= dydx=−yx=−1 (for point (-2,-2)).

For 2nd one, x+ydydx=0 so (let) s2 dydx=−xy=−1 (for(-2,-2)).

Now,

tanθ=|s1−s21+s1×s2|

Since s1=s2 , they cut at 0° angle, actually they touch each other.

Answer 2

please mark the above answer as brainliest

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