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If the tangent to the curve 2y^(3)=ax^(2...

If the tangent to the curve `2y^(3)=ax^(2)+x^(3)` at the point (a,a) cuts off intercept ` alpha and beta ` on the co-ordinate axes , (where ` alpha^(2)+beta^(2)=61`) then ` a^(2)` equals ______

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To solve the problem, we need to find the value of \( a^2 \) given the curve \( 2y^3 = ax^2 + x^3 \) and the conditions related to the tangent at the point \( (a, a) \). ### Step 1: Find the slope of the tangent line at the point \( (a, a) \) We start by differentiating the given curve implicitly with respect to \( x \). 1. Differentiate \( 2y^3 \) with respect to \( x \): \[ ...
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