Question

Can you please answer the whole page I’ll give you all the points I have and Brainiest answer

Answer 1

QUESTION 1

The given circle has equation:

$x^2+y^2=16$

We can rewrite to obtain;

$(x-0)^2+(y-0)^2=4^2$

This is equation is now in the form;

$(x-h)^2+(y-k)^2=r^2$

Where (h,k)=(0,0) is the center of the circle and $r=4$ is the radius.

QUESTION 2

The center of the circle is at (1,1) and passes through the point (4,5).

The radius of this circle is given by;

$r=\sqrt{(4-1)^2+(5-1)^2}$

$r=\sqrt{(3)^2+(4)^2}$

$r=\sqrt{9+16}$

$r=\sqrt{25}$

$r=5$ units.

We substitute into the formula;

$(x-h)^2+(y-k)^2=r^2$

$(x-1)^2+(y-1)^2=5^2$

$(x-1)^2+(y-1)^2=25$

Expand if you wish;

$x^2-2x+1+y^2-2y+1=25$

$x^2+y^2-2x-2y+2-25=0$

$x^2+y^2-2x-2y-23=0$