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Find the equation of the tangent and normal to the curve `16x^(2) + 9y^(2) = 144 at (x_(1), y_(1))`, where `x_(1) = 2 and y_(1) gt 0`. Also, find the points of intersection, where both tangent and normal cuts X-axis.

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The correct Answer is:
Equation of tangent is `8x + 3 sqrt(5)y = 36` meet at X-axis at `((9)/(2), 0)` and equation of normal is `24y - 9 sqrt(5)x = 14 sqrt(5)` meet X-axis at `(-(14)/(9), 0)`.
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ARIHANT PUBLICATION-APPLICATION OF DERIVATIVES -CHAPTER PRACTICE (SHORT ANSWER TYPE QUESTIONS )
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