x^2 y^2=81, (1,-9)

This is a circle with centre (0,0) and radius 9

the slope of the line diameter joining (0,0) and (1,-9) is -9-0/1-0 = -9

Hence tangent has gradient 1/9 (product of slopes of perpendicular lines = -1)

Equation of tangent line is y-y1= m(x-x1)

y + 9 =1/9 (x -1)

y = 1/9x - 9 -1/9

y = 1/9x -9 1/9

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