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If the normals at four points (x_(1),y_(1)),(x_(2),y_(2)), (x_(3),y_(3)) and (x_(4),y_(4)) on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 are concurrent then sumcosalpha.sumsecalpha is (where alpha, beta, gamma, delta are the eccentric angles of the points):

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Solution :d
`(a^(2)-b^(2))x^(4)-2ha^(2)(a^(2)-b^(2))x^(3)-x^(2)+2a^(4)H(a^(2)-b^(2))-a^(6)h^(2)=0implies(sumx_(1))(sum1/(x_(1)))=4`


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