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Find the equation of the tangents to the ellipse 2x^{2}+y^{2}=8\, is perpendicular to x+y+2=0\,

The equation of the tangent is y=mx\pm {\sqrt  {a^{2}m^{2}+b^{2}}}\,


y=mx\pm {\sqrt  {4m^{2}+8}}\,

The slope of the equation x+y+2=0\, is


Since the tangent of the ellipse is perpendicular to the above line,product of their slopes is -1


Hence the equation of the tangent is y=x\pm {\sqrt  {12}}\,

x-y\pm 2{\sqrt  {3}}=0\,

Main Page:Geometry:The Ellipse