Intersecting lines,circles,and parabolas

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AI Thread Summary
To find the intersection points of the line y=2x and the circle x^2+y^2=1, substitute y into the circle's equation to form a quadratic equation. Solving this quadratic will yield two x-values, which can then be used to find the corresponding y-values. It's clarified that the second equation is a circle, not a parabola, and the focus should be on solving the equations rather than the geometric interpretation. The discussion emphasizes the importance of finding real solutions for the intersection points. Understanding the method to solve these equations is key to determining the intersection points accurately.
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Homework Statement



find the points in which the graphs intersect

Homework Equations



y=2x, x^2+y^2=1

The Attempt at a Solution



the center point of the circle is (0,0)
and the radius = 1
and i collect some points to draw the line equation
(-1,-2) (0,0) (1,2) (2,4) etc ..

but i don't know how to get the intersect points ..
and also for the parabola equation ... are they have same way to know the intersect points ...
is there a rule or what ??
please explain to me in simple english words..

thanx a lot ...
 
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Just solve for x and y. Plug y = 2x into
x2+y2=1
to get
x2+(2x)2=1

Solve for x (you should get two solutions), and plug both into
y = 2x
to get the corresponding solutions for y.

Sumaya said:
and also for the parabola equation ... are they have same way to know the intersect points ...
is there a rule or what ??
The 2nd equation is an equation of a circle, not a parabola.
 
In simple English (nicht Deutsch, warum?), don't worry about the geometry, solve the equations!

If the problem were to find the intersection of x^2+ y^2= 1 and y= x^2, the first is a circle and the second a parabola. That's nice to know (it tells us we can expect to find two points of intersection) but not necessary to the solution. Since y= x^2 we can replace x^2 by y in the first equation: y+ y^2= 1 or y^2+ y- 1= 0. That's a quadratic equation and we can either complete the square or use the quadratic formula to solve for y. Once we have found y, x is a square root.

(The quadratic equation has two roots, of course, and you might think that since each has two roots, there would be 4 (x, y) combinations. But one of the (real) roots to the quadratic is negative. That gives only imaginary roots and coordinates of points in a graph must be real. Only y> 0 gives the two points of intersection.)
 
eumyang said:
Just solve for x and y. Plug y = 2x into
x2+y2=1
to get
x2+(2x)2=1

Solve for x (you should get two solutions), and plug both into
y = 2x
to get the corresponding solutions for y.


The 2nd equation is an equation of a circle, not a parabola.

thanx a lot ...
 
HallsofIvy said:
In simple English (nicht Deutsch, warum?), don't worry about the geometry, solve the equations!

you are right ..

and i undestand how to solve the equation ...

thanx a lot ..
 

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