Doug C. answered • 03/10/19

Math Tutor with Reputation to make difficult concepts understandable

Baofei L.

asked • 03/10/19Consider the circle with equation x^2+y^2-4y=0 and the point P(5,2). Draw a diagram to show the circle and the two lines from P that are tangent to the circle. Find the angle between the two tangent lines, angle APB, where A and B are the two points of contact.

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Doug C. answered • 03/10/19

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Math Tutor with Reputation to make difficult concepts understandable

Use completing the square to put the equation of the circle into standard form:

x^{2 }+ y^{2 }- 4y = 0

x^{2 }+ y^{2 }- 4y + 4 = 4

x^{2 }+ (y - 2)^{2 }= 4

Circle center is (0,2) with radius of 2

sin(θ) = 2/5

θ = sin^{-1}(2/5) = 23.58°

The angle between the 2 lines is 2θ = 47.16°

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