|
Question 289185: The circle x^2+y^2-6x-8y=0 intersects the y axis at A& B and is a tangent to the x axis at C.
(a) write down the coordinates of pt C
(b) find the length of the chord AB
i figured that a line or something touches (6,8) i think because of -6x and -8y
thx!!!!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The circle x^2+y^2-6x-8y=0 intersects the y axis at A& B and is a tangent to the x axis at C.
--------------
Complete the square to find the center and radius of the circle:
x^2-6x+9 + y^2-8y+16 = 25
(x-3)^2 + (y-4)^2 = 25
center at (3,4); radius = 5
-----------------
Draw the picture of that circle putting the center at (3,4)
and making the radius = 5.
------
y-intercepts = ?
Let x = 0 and solve for "y":
y^2-8y = 0
y(y-8) = 0
y = 0 or y = 8
---
The y-intercepts are (0,0) and (0,8)
The chord AB has length = 8
---------------------------------------
(a) write down the coordinates of pt C
Note: The circle is not tangent to the x-axis.
C is directly below (3,4)
C is (3,0) if it is on the x-axis
--------------------------
(b) find the length of the chord AB: 8
==============================================
Cheers,
Stan H.
==============================================
|
|
|
| |
