SOLUTION: Please help me solve this problems: 1.A circle whose centre lies on the line y=3x-1, touches both axes: find: (A) the equation of the circle (B) the points where the circle i

Question 841777: Please help me solve this problems:
1.A circle whose centre lies on the line y=3x-1, touches both axes:
find:
(A) the equation of the circle
(B) the points where the circle intersects the line 2y+x=1
2.Find the equation of the circle which passes through the points (0,3), (-1,2) and (7,-4)
3.A circle passes through the points (1,-15) and (-11,3). Its centre lies on the line 5y-12x+22=0. Find the coordinates of the centre, the radius and the equation of the circle.
4.The circle X^2 + Y^2 + 2x - 4y - 11 = 0 and the line X-y+1=0 intersect at A and B.Find the equation of the circle having AB as diamater.

Thank you in advance!
Best regards,
Kalin Mihow
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
1.A circle whose centre lies on the line y=3x-1, touches both axes:
find:
(A) the equation of the circle
-------------------
If by "touches" you mean tangent, then the center has to be on the line y = x to be equidistant from both axes.
Find the intersection of y=3x-1 and y = x. Call it (h,k)
----
The radius of the circle is the distance, h.
The eqn is
---------------
(B) the points where the circle intersects the line 2y+x=1
Solve for the 2 points.
==============================================
2.Find the equation of the circle which passes through the points (0,3), (-1,2) and (7,-4)
Do you know about determinants?
------------------------------
3.A circle passes through the points (1,-15) and (-11,3). Its centre lies on the line 5y-12x+22=0. Find the coordinates of the centre, the radius and the equation of the circle.
Try it, email via the Thank You note for help or to check your work.
--------------------
4.The circle X^2 + Y^2 + 2x - 4y - 11 = 0 and the line X-y+1=0 intersect at A and B. Find the equation of the circle having AB as diamater.
Try it, email via the Thank You note for help or to check your work.

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