Answer:
[tex]x^2+y^2-41=0[/tex]
Step-by-step explanation:
Center of the circle is (0,0)
the point on the circle is (4,5)
Center radius form of the circle is
[tex](x-h)^2 +(y-k)^2= r^2[/tex]
where (h,k) is the center and 'r' is the radius of the circle
WE know center is (0,0) . Lets find out the radius using the given point
[tex](x-0)^2 +(y-0)^2= r^2[/tex]
[tex]x^2+y^2= r^2[/tex]
Plug in the given point (4,5)
[tex]4^2+5^2= r^2[/tex]
[tex]16+25= r^2[/tex]
[tex]41=r^2[/tex]
Equation becomes
[tex]x^2+y^2=41[/tex]
General form of equation is
[tex]x^2+y^2+gx+fx+c=0[/tex]
[tex]x^2+y^2=41[/tex]
[tex]x^2+y^2-41=0[/tex]
