Homework Help: Calculus

Posted by George on Friday, November 7, 2008 at 12:43am.

(A) Find the equations of the tangent lines to the circle x^2 +y^2=25 at the points where x=4.
(B) Find the equations of the normal lines to this circle at the same points. (The normal line is perpendicular to the tangent line at that point.)
(C) At what point do the two normal lines intersect?

For part A, I found that
16 + y 2= 25
y 2= 9
y=3
y=3/4x
For part B,I'm not sure whether it is y=-4/3x
For part C Not sure how to do it.

Calculus - asia, Friday, November 7, 2008 at 3:02am
I solved the question in A but please check..
first of all you have to find y while x=4 and as you find y^2=25-16=9 and y=3
then you have to find slope. It's derivative of y function so
(slope)m=1/2(1/25-x^2)(2x).
if we write 3 instead of x we will get m(slope) as -4/3.
from
the tangent line equation
y-3=(-4/3)(x-4)
y=(-4/3)x+25/3.(result)
Calculus - asia, Friday, November 7, 2008 at 4:00am
solution for part B
for the normal line equation firstly you have to find again slope. product of tangentline's slope and normal line's slope must be -1.
there fore
line's slope.(-4/3)=-1
line's slope= 3/4
then
the line equation is
y-3= =(3/4)(x-4)
we get
y= 3x/4(result)

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