With the equation x 2 + 2 x y − 3 y 2 + 16 = 0, I need to find the coordinates of the points on the curve where d y d x = 0. I think I have correctly used implicit differentiation to get d y d x = − x − y x − 3 y . And the multiplied by the denominator and subsituted zero to get, 0 = − x − y, however, I'm not sure where to go from here.If anyone could help that would be great. Thanks.

Question

With the equation       x    2    +  2  x  y  −  3      y    2    +  16  =  0, I need to find the coordinates of the points on the curve where             d      y              d      x        =  0. I think I have correctly used implicit differentiation to get             d      y              d      x        =            −      x      −      y              x      −      3      y      . And the multiplied by the denominator and subsituted zero to get,   0  =  −  x  −  y, however, I&#039;m not sure where to go from here.If anyone could help that would be great. Thanks.

Gauge Howard · Accepted Answer

At the point where   (  x  ,  y  ) where   d  y      /    d  x  =  0, it follows that   y  =  −  x. To find   x and   y, note that      x    2    +  2  x  (  −  x  )  −  3  (  −  x      )    2    +  16  =  0Solve for   x and substitute into   y  =  −  x to find   y.

opositor5t · Accepted Answer

Hint: The point is on the curve, so it also satisfies       x    2    +  2  x  y  −  3      y    2    +  16  =  0.

With the equation x^2+2xy−3y^2+16=0, I need to find the coordinates of the points on the curve where (dy)/(dx)=0.

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