Let p be the number of all triangles that can be formed by joining the vertices of a regular polygon P of n sides and q be the number of all quadrilaterals that can be formed by joining the vertices o

Question

Let p be the number of all triangles that can be formed by joining the vertices of a regular polygon P of n sides and q be the number of all quadrilaterals that can be formed by joining the vertices of P . If p + q = 126 , then the eccentricity of the ellipse 16 x 2 ​ + n y 2 ​ = 1 is :

TestHub · Accepted Answer

​ Total trangles =⇒= h C 3 ​ Total auadrilaterals = h C 4 ​ = q n C 3 ​ + n C 4 ​ = 126 ⇒ n + 1 C 4 ​ = 126 ⇒ n + 1 = 9 ⇒ n = 8 16 x 2 ​ + n y 2 ​ = 1 ⇒ 16 x 2 ​ + 8 y 2 ​ = 1 e = 1 − 16 8 ​ ​ = 16 8 ​ ​ = 2 ​ 1 ​ ​

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