The ellipse ( x^ 2 (m+1)^ 2 + y^ 2 m^ 2 =1 ) ((m>0) ) is known to have eccentricity (…

MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

The ellipse x2(m+1)2+y2m2=1\dfrac{x^{2}}{(m+1)^{2}}+\dfrac{y^{2}}{m^{2}}=1 (m>0)(m>0) is known to have eccentricity 45\dfrac{4}{5}. (i) Show that mm satisfies a linear equation and find its positive value. (ii) Using this value of mm, write the standard form of the ellipse with explicit numerical denominators. (iii) Determine the coordinates of its foci and the length of the major axis. (iv) Find the eccentricity again from your results in part (iii) to confirm that it equals 45\dfrac{4}{5}.

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