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Intersection of conics
CONCEPTS
There are 2 ways to determine how figures intersect
1) Set the y's equal to one another for the 2 equations to determine the x-point of intersection. Put that x-value back into either equation to determine the y-coordinate of intersection.
2) Plot out the figures
PRACTICE PROBLEMS
Question 1 Given a circle & ellipse equation. Where do they intersect?
Circle: x² + y² = 4
Ellipse: x² / 4 + (y – 1)² / 9 = 1?
-- Answer -- -2 & 2/5
1) set a variable equal to each other or 2) graph it out
x² = 4 – y² & x² = (1 – (y – 1) ² / 9) ⋅ 4
4 – y² = 4 – 4 / 9 (y – 1)², y² – 4 / 9 (y–1)²=0
5y² + 8y – 4 = 0, y = –2 & 2/5
graphing –> too difficult to find points
ACT PRACTICE PROBLEMS
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