10. Line m is tangent to circle O at the point (12, -9.) If the center of O is at the origin, what is the y-intercept of line m?

Note: I have already established that the radius is 15.

Thank you :)

Question

10. Line m is tangent to circle O at the point (12, -9.) If the center of O is at the origin, what is the y-intercept of line m?

Note: I have already established that the radius is 15.

Thank you :)

anonymous · Answer

What you can do in this situation is 
|dw:1455576125375:dw|

anonymous · Answer

Any tangent line is perpendicular to the radius of a circle
So what is the slope of the radius in this case?

albert0898 · Answer

@Brill The slope is -3/4

anonymous · Answer

ok so the slope of a line perpendicular to a line is the NEGATIVE RECIPROCAL
So for example if you had a line of slope 20, the slope of a line perpendicular to that would be -1/20

anonymous · Answer

So what would the slope of the line be?

albert0898 · Answer

4/3

albert0898 · Answer

@Brill

anonymous · Answer

Yup, now you can input that into point slope form, input the point and find the y intercept

anonymous · Answer

Do you know how to do that?

albert0898 · Answer

@Brill 
Well, point-slope form is y − y1 = m(x − x1)

albert0898 · Answer

y+9 = 4x/3 - 48/3

albert0898 · Answer

y = 4x/3 - 25

anonymous · Answer

Yup
So you would get
$$y-(-9)=\frac{ 4 }{ 3 }(x-12)$$

albert0898 · Answer

Thank you for your help @Brill  :)

anonymous · Answer

You want the y intercept, and at the y intercept x always equals 0
So sub 0 for x and solve for y

anonymous · Answer

No problem :)