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Find the points on the ellipse (x^2)/(a^...

Find the points on the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` such that the tangent at each point makes equal angles with the axes.

Text Solution

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Sinece tangests make equal angles with the axes, their slope i.e., should be `+-1`
Ponts of contant of tanget having slop 'm' are given by `((+-a^(2)m)/(sqrt(a^(2)m^(2)+b^(2))),(+-b^(2))/(sqrt(a^(2)m^(2)+b^(2))))*`
For m=1 ponts of contant are `((a^(2))/(sqrt(a^(2)+b^(2))),(-b^(2))/(sqrt(a^(2)+b^(2))))and ((-a^(2))/(sqrt(a^(2)+b^(2))),(b^(2))/(sqrt(a^(2)+b^(2))))`
For m-1 , points of contant are `((a^(2))/(sqrt(a^(2)+b^(2))),(b^(2))/(sqrt(a^(2)+b^(2))))and ((-a^(2))/(sqrt(a^(2)+b^(2))),(-b^(2))/(sqrt(a^(2)+b^(2))))`
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