Geometry math problem? Need help!?

Question

An equation for the circle that has its center at the origin & passes through the point (3,4) is

Answer is

x^2+y^2=25

But WHY!?

Answer 1

x^2+y^2=r^2 is the equation with r as the radius

plug x=3, y=4

3^2+4^2=9+16=r^2

25=r^2

r=5

x^2+y^2=25

Answer 2

Umm I haven't been in school for a while since it's summer and I'm not sure what the question means but I will try to help. Since the point is (x=3,y=4) that would mean that x^2+y^2=25 really means (3^2(Which is 9))+(4^2(Which is 16))=25

9+16=25

Hope this helps and if it doesn't, I sorry because like I said I haven't been in school for a while because it's summer break right now.

Answer 3

general equation of a circle --->

(x - x1)2 + (y - y1)^2 = radius^2 where centre is (x1, y1)

The points (3,4) and (0,0) form a right angled triangle with the x axis where 4 is the height and 3 is the base of the triangle. Find the third side (the radius) by pythagoras ...

(3)^2 + (4)^2 = r^2

=> 25 = r^2

=> r = 5 (radius can't be negative so we ignore -5)

there you have it ...

(x - 0)^2 + (y - 0)^2 = 25 (radius squared)

=> x^2+y^2=25

Answer 4

Because the distance from the origin of a circle to ANY point on the circle is x^2+y^2.   The locus of all points with the same sum of squares is the circle.  The sum of squares is the constant on the right-hand side.  

Answer 5

it would probably be easier to explain w/ a white board but i'll give it a shot....

for circle graphs in form x^2 + y^2=n, the radius of the circle is the square root of n. So in this problem the radius would be 5.

secondly, with the graph going through point (3,4), it would create a triangle between points (0,0), (3,0), and (0,4) because of pythagorean theorem (i.e. 3^2 + 4^2 = 5^2)

that's pretty much the whole reasoning behind it i think. i hope this solves your confusion.