Find the equation of the tangent of the ellipse x^2/a^2 + y^2/b^2 = 1 whose slope is "m"
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The line y = mx + c meets the ellipse x2/a2 + y2/b2 = 1 in two real, coincident or imaginary points according as c2 < = or > a2m2 + b2.
Hence, y = mx + c is tangent to the ellipse x2/a2 + y2/b2 = 1 if c2 = a2m2 + b2.
The equation of the chord to the ellipse joining two points with eccentric angles α and β is given by
x/a cos ((α + β)/2) + y/b sin ((α + β)/2) = cos ((α - β)/2)
Hence, y = mx + c is tangent to the ellipse x2/a2 + y2/b2 = 1 if c2 = a2m2 + b2.
The equation of the chord to the ellipse joining two points with eccentric angles α and β is given by
x/a cos ((α + β)/2) + y/b sin ((α + β)/2) = cos ((α - β)/2)
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