How do you find the equations for the normal line to #x^2+y^2=25# through (4,3)?

Answer 1

#y=3/4x#

This is the equation of a circle with center in the origin and #R=5#.
For the properties of the circle, the radius is normal to the tangent, so the normal line will pass through #(0,0)# as well as through #(4,3)# and its equation is given by:
#y=3/4x#
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Answer 2

To find the equation of the normal line to the circle (x^2 + y^2 = 25) at the point (4, 3):

  1. Find the derivative of the equation of the circle with respect to (x).
  2. Evaluate the derivative at the point (4, 3) to find the slope of the tangent line.
  3. Find the negative reciprocal of the slope to get the slope of the normal line.
  4. Use the point-slope form of a line to find the equation of the normal line using the slope found in step 3 and the point (4, 3).
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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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