- #1
jeahomgrajan
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Homework Statement
This is a simple math equation and i am a bit confused on how
x^2+y^2=25 makes a circle and how y= sqrt 25-x^2 makes a semi circle
No, not quite. (Keep in mind that [tex]\sqrt{a^{2}-b^{2}}\neq a-b[/tex].)jeahomgrajan said:y=5-x
jeahomgrajan said:y=5-x ( that would make a semi circle right)
jeahomgrajan said:+-3?
The equation x^2 + y^2 = 25 represents a circle with a radius of 5 and a center at the origin (0,0).
The solutions to this equation are all real values of x that make the expression under the square root positive. This includes all values of x between -5 and 5, as well as the two endpoints (x = -5 and x = 5).
Changing the value of x will shift the graph of this equation horizontally. As x increases, the circle will shift to the right, and as x decreases, the circle will shift to the left.
The first equation represents a circle with a radius of 5 and a center at the origin. The second equation represents a semicircle with the same radius and center, but only the top half is graphed due to the square root function. Both equations have the same solutions, but they have different graphs.
Yes, we can solve this system of equations graphically by finding the points where the circle and semicircle intersect. The solutions are (0,5) and (0,-5).