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If the curves (x^(2))/(a^(2))+(y^(2))/(...

If the curves ` (x^(2))/(a^(2))+(y^(2))/(4)=1 and y^(3)=16x` intersect at right angles , then ` 3a^(2)` is equal to ________

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To solve the problem, we need to find the value of \(3a^2\) given that the curves \(\frac{x^2}{a^2} + \frac{y^2}{4} = 1\) and \(y^3 = 16x\) intersect at right angles. ### Step-by-step Solution: 1. **Differentiate the first curve**: The first curve is given by: \[ \frac{x^2}{a^2} + \frac{y^2}{4} = 1 ...
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