SOLUTION: I need to find the intersection points of a circle and an ellipse. Circle: x^2 + (y-9)^2 = 16 Ellipse: x^2/16 + (y-1)^2/49 = 1 Please help me out. This is for a project, it

Click here to see ALL problems on Quadratic-relations-and-conic-sections

Question 198157: I need to find the intersection points of a circle and an ellipse.
Circle: x^2 + (y-9)^2 = 16
Ellipse: x^2/16 + (y-1)^2/49 = 1
Please help me out. This is for a project, it is not in a book.
Found 2 solutions by stanbon, vleith:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
I need to find the intersection points of a circle and an ellipse.
Circle: x^2 + (y-9)^2 = 16
Ellipse: x^2/16 + (y-1)^2/49 = 1
----------------
Solve the circle equation for x^2 : x^2 = [16 - (y-9)^2]
----------
Get rid of the denominators on the ellipse equation by multiplying
thru by 16*49 to get:
49x^2 + 16(y-1)^2 = 16*49
-------------------
Substitute "x^2"-value into the ellipse equation to get:
---
49[16 - (y-9)^2] + 16[y^2-2y+1] = 16*49
49*16 - (y^2 - 18y + 81) + 16y^2 - 32y + 16 = 16*49
---
Subtract 16*49 from both sides and do some simplifying to get:
-y^2 + 18y - 81 + 16y^2 - 32y + 16 = 0
Simplify some more:
15y^2 - 14y - 65 = 0
(3x+5)(5x-13) = 0
x = -5/3 and x = 13/5 are the x-values of the points of intersection.
-------------
Substitute those values into x^2 = 16 - (y-9)^2 to find the
corresponding y-values.
=========================================
Cheers,
Stan H.

Answer by vleith(2983) (Show Source):
You can put this solution on YOUR website!
You are asked to find the points that intersect. So you are being asked to find the values for x and y that satisfy both equations.

Sub that into the second equation

http://www76.wolframalpha.com/input/?i=(16+-+(y-9)^2+)%2F16++%2B+(y-1)^2%2F49+-1+%3D+0
Now use those values for y to find the value for x
You could also go get geogebra and use that to find the intersecting points