Respuesta :
Answer:
A. Standard form: [tex](x-8)^2+(y-9)^2=100[/tex]
B. General form: [tex]x^2+y^2-16x-18y+45=0[/tex]
Step-by-step explanation:
We have been given that center of a circle is at point (8,9) and radius of our circle is 10 units. We are asked to write the equation of our circle.
A. Since we know that the equation of a circle in standard form is: [tex](x-h)^2+(y-k)^2=r^2[/tex], where,
(x,y) = Any point on circle,
(h,k) = Center of the circle,
r = Radius of the circle.
Upon substituting our given values in standard form of circle's equation we will get,
[tex](x-8)^2+(y-9)^2=10^2[/tex]
[tex](x-8)^2+(y-9)^2=100[/tex]
Therefore, the equation of our given circle in standard form will be [tex](x-8)^2+(y-9)^2=100[/tex].
B. Since we know that equation of a circle in general form is: [tex]x^2+y^2+Ax+By+C=0[/tex], where, A, B and C are constants.
Upon expanding our standard form of equation we will get,
[tex]x^2-16x+64+y^2-18y+81=100[/tex]
[tex]x^2-16x+64+y^2-18y+81-100=100-100[/tex]
[tex]x^2-16x+y^2-18y+64+81-100=0[/tex]
[tex]x^2-16x+y^2-18y+45=0[/tex]
[tex]x^2+y^2-16x-18y+45=0[/tex]
Therefore, the equation of our given circle in general form will be [tex]x^2+y^2-16x-18y+45=0[/tex].
