Exercise 24 Page 801

To begin, let's recall the Distance Formula. This formula is used to find the distance d between two points (x_1,y_1) and (x_2,y_2). d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2) We will find the radius of our circle by substituting the given points into this formula and finding the distance between the center and the known point through which the circle passes.

d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)

SubstitutePoints

Substitute ( -1,-4) & ( -4,0)

d=sqrt(( -4-( -1))^2+( 0-( -4))^2)

▼

Evaluate right-hand side

SubNeg

a-(- b)=a+b

d=sqrt((-4+1)^2+(0+4)^2)

AddTerms

Add terms

d=sqrt((-3)^2+4^2)

CalcPow

Calculate power

d=sqrt(9+16)

AddTerms

Add terms

d=sqrt(25)

CalcRoot

Calculate root

d=5

Let's now recall the standard form of an equation of a circle. (x- h)^2+(y- k)^2= r^2 In this formula, ( h, k) is the center of the circle and r is its radius. We are told that the center of the circle is ( -1, -4). This information, together with r= 5, is enough to write the equation. (x-( -1))^2+(y-( -4))^2= 5^2 ⇕ (x+1)^2+(y+4)^2=25