Question

I only need help with part B of question 7

Answer 1

Question:

Solution:

An equation in the standard form of the circle with center (h,k) and radius r is given by the following formula:

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

a)

Consider the following circle equation:

$(x+5)^2+(y-2)^2=10^{}$

According to the standard form equation for a circle, we can conclude:

Center of the circle = (-5, 2)

The radius of the circle = √10

b) According to the standard form equation for a circle, we have that a circle with center (-5, 2 ) will have the following provisional equation:

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

to find r, we can use the coordinates of the point (x,y)=(2,-1) into the above equation and solve for r:

$(2+5)^2+(-1-2)^2=r^2$

this is equivalent to:

$(7)^2+(-3)^2=r^2$

this is equivalent to:

$r^2=58$

solving for r, we obtain:

$r=\sqrt[]{58}$

so that, we can conclude that the equation of the circle would be:

$(x+5)^2+(y-2)^2=58$