Consider the curve given by the equation y2=x2+33 (where y > 0). The y-intercept of the normal line drawn to the curve at x = 4 is

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Consider the curve given by the equation $y^{2} = x^{2} + 33$ (where y > 0). The y-intercept of the normal line drawn to the curve at x = 4 is

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Detailed Solution

At $x = 4; y = 7$ (As $y > 0$ )
$y^{2} = x^{2} + 33 2 yy' = 2 x y' = \frac{4}{7}$
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$∴ m_{normal} = \frac{- 7}{4}$
equation of normal is $(y - 7) = \frac{- 7}{4} (x - 4)$
y-intercept $\Rightarrow x = 0; y = 7 + 7 = 14$

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