"Two circles have equations ofx2+y2−4x−4y+4=0x2+y2−4x+8y+4=0Find the distance between..." was answered by students like you

Keri Molloy

Answered question

2022-02-28

Two circles have equations of

x^{2} + y_{2} - 4 x - 4 y + 4 = 0

x^{2} + y^{2} - 4 x + 8 y + 4 = 0

Find the distance between the centers of the two circles.

jexExtiftlot

Beginner2022-03-01Added 5 answers

Step 1
Equations of two circles are:

C_{1} : x^{2} + y^{2} - 4 x - 4 y + 4 = 0

C_{2} : x^{2} + y^{2} - 4 x + 8 y + 4 = 0

Converting these equations in theria standard form

C_{1} : x^{2} + y^{2} - 4 x - 4 y + 4 = 0

x^{2} - 4 x + 4 + y^{2} - 4 y + 4 = 4

C_{1} : {(x - 2)}^{2} + {(y - 2)}^{2} = {(2)}^{2}

C_{2} : x^{2} + y^{2} - 4 x - 8 y + 4 = 0

x^{2} - 4 x + 4 + y^{2} - 8 y + 16 = 16

C_{2} : {(x - 2)}^{2} + {(y - 4)}^{2} = {(4)}^{2}

Step 2
In

C_{1}

, Centers is (2, 2) and radius

= 2

C_{2}

, Centers is (2, 4) and radius

= 4

Therefore distance

\frac{b}{w}

the Centers is given by:

d = \sqrt{{(4 - 2)}^{2} + (2 - 2)} = \sqrt{4} = 2

d = 2

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