Geo5.2.16

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Find the equation of tangents to the ellipse 2x^{2}+y^{2}=8\, which is parallel to x-2y-4=0\,.

The tangent to the ellipse is parallel to the line x-2y-4=0\,

-2y=-x+4,2y=x-4\,

Hence the slope of the required tangent is equal to the slope of the given line.

Therefore,the slope of the required tangent is 1/2.

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

From the given ellipse a^{2}=4,b^{2}=8\,

The equation of the tangent is

y={\frac  {1}{2}}(x)\pm {\sqrt  {4\cdot {\frac  {1}{4}}+8}}\,

y={\frac  {x}{2}}\pm 3\,

2y-x=\pm 6\,


Main Page:Geometry:The Ellipse