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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(ygt 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) = 2x rArr (dy)/(dx) = (x)/(y)` where x = 4 , y = 7 (y gt 0)`
`therefore (dy)/(dx) = (4)/(7)`
`therefore` Slope of the normal = `(-7)/(4)`
Equation of normal is y - 7 = `(-7)/(4) (x - 4)` if x = 0 , y - 7 = 7 `rArr y = 14`
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