Find all points on the curve x 2 y 2 + x y = 2 where the slope of the tangent line is -1.

Question

Find all points on the curve                   x        2                    y        2            +      x      y      =      2       where the slope of the tangent line is -1.

a4dlity3v · Accepted Answer

Angle OBA = 90 degrees(By theorem, the radius across the point of contact is perpendicular to the tangent at any point on a circle.)Pythagoras theorem in right angled ABO    &amp;#x21D2;    O          B      2        =    O          A      2        &amp;#x2212;    A          B      2                  r      2        =    (    r    +    7.5          )      2        &amp;#x2212;          15      2            r    2    =          r      2        +    56.25    +    15    r    &amp;#x2212;    225        15    r    =    168.75        r    =    11.25    c    m        &amp;#x2234;    D    i    a    m    e    t    e    r    =    2    r    =    2    &amp;#xD7;    11.25    =    22.5    c    m

Find all points on the curve x 2 y 2 + x y = 2...

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