SOLUTION: circle with equation: X^2 + Y^2 - 6X - 18Y + 45
Tangent touches the circle at point T equation of the tangent is 2Y = X
Show algebraically that T has coordinates (6,3).
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-> SOLUTION: circle with equation: X^2 + Y^2 - 6X - 18Y + 45
Tangent touches the circle at point T equation of the tangent is 2Y = X
Show algebraically that T has coordinates (6,3).
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Question 141508: circle with equation: X^2 + Y^2 - 6X - 18Y + 45
Tangent touches the circle at point T equation of the tangent is 2Y = X
Show algebraically that T has coordinates (6,3). Answer by Edwin McCravy(20086) (Show Source):
You can put this solution on YOUR website! circle with equation:
Tangent touches the circle at point T equation of the tangent is
Show algebraically that T has coordinates (6,3).
Just solve the system
by substitution
Substitute 2Y for X in the first:
Divide every term by 5
Factor:
(Y-3)(Y-3)=0
gives gives
[The fact that we get only one solution tells us
that the line touches the circle in only one
point. So this proves that it is indeed tangent]
Now to find
Substitute for in
6=X
So the point of tangency is (6,3)
Edwin
