SOLUTION: Find the lengths of the tangents (8,3) to each circle a) x^2+y^2 =9 b) x^2+y^2=36 c) x^2 + y^2 = 65 Can you please help me out? Thanks so much in advance:) Can you also please

Question 795364: Find the lengths of the tangents (8,3) to each circle
a) x^2+y^2 =9
b) x^2+y^2=36
c) x^2 + y^2 = 65
Can you please help me out? Thanks so much in advance:)
Can you also please show the steps it would really help me understand:)
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find the lengths of the tangents (8,3) to each circle
a) x^2+y^2 =9
b) x^2+y^2=36
c) x^2 + y^2 = 65
----------
All 3 circles have the center at (0,0).
a) x^2+y^2 =9
Has a y-intercept of (0,3).
--> length = 8 units.
===========================
b) x^2+y^2=36
The line from (0,0) is the hypotenuse of a right triangle formed by (0,0), (8,3) and the tangent point.
Hyp = sqrt(73)
Radius = 6
---
t = tangent length
6^2 + t^2 = 73
t = sqrt(37)
---
c) x^2 + y^2 = 65
t = sqrt(8)
------------------
The tangent points were not asked for.

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