Geo5.2.14

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Find the equations of tangent snd normal to the ellipse 2x^{2}+3y^{2}=11\, at the point whose ordinate is 1.

Let P(x_{1},y_{1})\, be a point on the ellipse whose ordinate is 1.

Therefore P(x_{1},1)\, is a point on the ellipse 2x^{2}+3y^{2}=11\,

Hence 2x_{1}^{{2}}+3=11,x_{1}=\pm 2\,

Therefore coordinates of P are (2,1),(2,-1)\,

The equation of the tangent at (2,1)\, is 4x+3y=11\,

The equation of the tangent at (-2,1)\, is 4x-3y+11=0\,

The equation of the normal at (2,1)\, is {\frac  {11x}{4}}-{\frac  {11y}{3}}={\frac  {11}{2}}-{\frac  {11}{3}}\,

By simplifying

33x-44y=22,3x-4y=2\,

The equation of the normal at(-2,1)\, is {\frac  {11x}{-4}}-{\frac  {11y}{3}}={\frac  {11}{2}}-{\frac  {11}{3}}\,

By simplifying

-33x-44y=22,3x+4y+2=0\,


Main Page:Geometry:The Ellipse