Tangent Lines (Choose multiple)

Question

a) choose the correct equation(s) of the tangent line(s) to the circle x^2 + y^2 = 25 at the points where x = 4.

1. y = 3 - 4/3(x-4)

2. y = -3 -4/3(x-4)

3. y = 3/4x

4. y = -3/4x

5. y = 3 + 4//3(x-4)

6. y = -3 + 4/3(x-4)

b) choose the correct equation(s) of the normal line(s) to this circle at same points. (The normal line is perpendicular to the tangent line at that point)

1. y = 3 - 4/3(x-4)

2. y = -3 + 4/3(x-4)

3. y = 3/4x

4. y = -3/4x

5. y = 4/3x

6. y = -4/3x

c) at what point do the two normal lines intersect?

Answer 1

Answer 2

At x = 4, y = ±3

At (4, 3) slope of tangent is -4 / 3, Use point-slope form

At (4, -3) slope of tangent is 4 / 3. Use point slope form

Tangents interesect when equation set to equal