Find the equation of the ciscle whose centre is at
(3,-4) and line 3x-4y-5=0 cuts the circle
at A and B. such that l(AB) = 6 units
Answers
Answer:Firstly:
A) The circle touches the [math]Y-Axis[/math] in [math]A(0,3)[/math], which means that[math] Y-Axis[/math] is a tangent line to it at [math]A[/math], yields that [math]E[/math] is located in a line parallel to [math]Y-Axis[/math] and passing through [math]A[/math]
B) That the circle intersects the[math] x-axis[/math] in [math](8,0)[/math], means either:
1) the point C has [math](0,8)[/math] as coordinates.
2) or The point B is the one that is located at those coordinates .
The first case is rejected by the first condition, meanwhile the second one is accepted.
So according to the figure above, in the right triangle [math]EDB,[/math] we find that:
[math]ED^2+DB^2 = EB^2[/math][math] [/math]it means that [math]3^2+(8-R)^2 = R^2[/math] , it yields that [math]R=\frac{73}{16}[/math]
Then the coordinates of [math]E[/math] are [math](R=\frac{73}{16} , 3)[/math]
Hence, the equation of the circle is:
[math] (x-\frac{73}{16})^2+(y-3)^2 = \frac{73^2}{16^2} [/math]
Step-by-step explanation:
