Answer:
The correct answer option is d. [tex]x^2+y^2-8x+4y-80=0[/tex]
Step-by-step explanation:
We are given the center of the circle at (4, -2) with a radius of 10 units and we are to find the equation of the circle with the help of this.
We know the standard form of the equation of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
So putting in the values of the coordinates of the center [tex](h, k)[/tex] and radius.
[tex](x-4)^2+(y+2)^2=10^2[/tex]
Expanding the formulas to get:
[tex](x^2+8x+16)+(y^2+4y+4)=100[/tex]
Adding the like terms together to get:
[tex]x^2-8x+y^2+4y+16+4-100=0[/tex]
[tex]x^2+y^2-8x+4y-80=0[/tex]
