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Calculus

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(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 -

    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 -

    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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