The first two equations are circles.
I'm not sure what the next four quantities represent.
Nor what the line in the last equation represents.
Whatever you are doing is unnecessary to check whether
What do those lines represent?
What's on the left of the 3rd = ?
Do you need to find the points of intersection, or just determine whether they intersect?
These are two circles that I have to check if they intersect or not?
'What's on the left of the 3rd = ?' Not sure which one you mean. Is it this bit =4 ( x + y - 2) if so thats a typo sorry there shouldn't be an eqauls there.
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The first two equations are circles.
I'm not sure what the next four quantities represent.
Nor what the line in the last equation represents.
Whatever you are doing is unnecessary to check whether they intersect or not.
For that, it is sufficient to determine the radius of each circle and the distance between their centres.
You can tell (just by looking at the two equations) that the radius of the first circle is 1
and the radius of the second circle is 2. Do you see this?
You can also tell (again just by looking) what the centers of the two circles are.
Do you know how to do this?
>> x^2 + y^2 = 4
>> isn't the radius 4 and the centre (2,2)?
Ok, you are saying that r = 4, x0 = y0 = 2.
Test out your idea by plugging in your values into the circle equation from the link:
(x - x0)² + (y - y0)² = r²
Write down the equation plugging in the values. The equation you come up with will be a circle whose center is (2,2) and whose radius is 4. Does this equation match the equation of the one you posted?
Here is an example that I am making up.(x + 19)² + (y - 17)² = 36We recognize the form of this equation as a circle having a center (x0,y0) and radius r. We want to find out these 3 values.The standard form of a circle (from the link) is: (x - x0)² + (y - y0)² = r² (x + 19)² + (y - 17)² = 36We need minus signs inside the parenthesis. Notice that +19 == -(-19), and that 36 == 6² , so rewrite as: (x + 19)² + (y - 17)² = 36 ==> (x - (-19) )² + (y - 17)² = 6² (x - x0 )² + (y - y0)² = r²By inspection, you can see that x0 is -19, y0 is 17, and r is 6; so we have a circle whose center is (-19, 6) and whose radius is 6.
correction to cut and paste error:By inspection, you can see that x0 is -19, y0 is 17, and r is 6; so we have a circle whose center is (-19, 17) and whose radius is 6.
To extract the center and radius from a circle convert it to
GENERIC EQUATION OF A CIRCLE
(x - x_0)² + (y - y_0)² = r²
form
For example,
(x - 3)^2 + (y+ 7)^2 = 100
becomes
(x - 3)^2 + (y - (- 7) )^2 = 10^2
Now it's identically in the generic form.
We can lift out x_0 = 3, y_0= -7 and the radius = 10.
So for the 2nd equation, x^2 + y^2 = 4
the center is not (2, 2) because there is no 2 being added or subtracted from x and no 2 being added or subtracted from y.
The radius is not 4. because it still needs to go into square form first. Only when we have the form
(x - x_0)² + (y - y_0)² = r²
can we directly find x_0, y_0 or r from the equation.
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