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Find points on the curve (x^2)/4+(y^2)/(...

Find points on the curve `(x^2)/4+(y^2)/(25)=1`at which the tangents are (i) parallel to x-axis (ii) parallel to y-axis.

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To solve the problem of finding points on the curve \(\frac{x^2}{4} + \frac{y^2}{25} = 1\) where the tangents are parallel to the x-axis and y-axis, we will follow these steps: ### Step 1: Differentiate the given equation We start with the equation of the ellipse: \[ \frac{x^2}{4} + \frac{y^2}{25} = 1 \] We differentiate both sides with respect to \(x\): ...
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