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The y-intercept of the line normal to th...

The y-intercept of the line normal to the curve `y^2=x^2+33(y gt 0)` at the point with abscissa 4 is :

A

7

B

10

C

14

D

15

Text Solution

Verified by Experts

The correct Answer is:
C
`y^(2) = x^(2) + 33 `
` 2y(dy)/(dx) = 2 x implies (dy)/(dx) = (x)/(y) ` where ` x =4 , y = 7 ( y gt 0)`
` :. (dy)/(dx) = (4)/(7)`
`:.` Slope of the normal `=(-7)/(4)`
Equation of normal is ` y-7 =(-7)/(4) (x-4)` if x = 0 , y - 7 =7 `implies` y = 14
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