SOLUTION: Question 1 The foci are at (+-2,0)and the ellipse passes through (2,-3) Question 2 The ellipse passes through points (6,4) and (-8,3) Question 3 Find the equation of the

Question 550205: Question 1
The foci are at (+-2,0)and the ellipse passes through (2,-3)
Question 2
The ellipse passes through points (6,4) and (-8,3)
Question 3
Find the equation of the circle which has its centre at point (2,3) and passes through the origin
Question 4
The centre of a circle lies on line y=2x-2, and this circle cuts the x-axis at points (1,0)and (3,0). Find the equation of the circle.

For question 3
This is what I've done:
(h,k)=(2,3)
(x-2)^2+(y-3)^2=r^2
(0-2)^2+(0-3)^2=r^2
4+9+r^2
r^2=13
R=√13
Please provide for me the full working as it is easy for me to understand, Thanks
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Question 1
The foci are at (+-2,0)and the ellipse passes through (2,-3)
Question 2
The ellipse passes through points (6,4) and (-8,3)
----------
An infinite # of ellipses can pass thru 2 points.
----------------
Question 3
Find the equation of the circle which has its centre at point (2,3) and passes through the origin
----------
For question 3
This is what I've done:
(h,k)=(2,3)
(x-2)^2+(y-3)^2=r^2
(0-2)^2+(0-3)^2=r^2
4+9+r^2
r^2=13
--> Which is correct.
-------------------
Question 4
The centre of a circle lies on line y=2x-2, and this circle cuts the x-axis at points (1,0)and (3,0). Find the equation of the circle.
----
The center has to be on a line bisecting the 2 points, which is x = 2.
Find the solution of
x = 2
y = 2x - 2
-----
--> (2,2)
---
Find r^2
r^2 = diffy^2 + diffx^2 = 1 + 4
-->

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