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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 step by step, we will analyze the given curve and find the required value of \( a^2 \). ### Step 1: Write the equation of the curve The given curve is \[ 2y^3 = ax^2 + x^3. \] ...
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