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For the next two (2) items that follow :

Consider the two circles

(x-1)^2+(y-3)^2=r^2

and

x^2+y^2-8x+2y+8=0

[NDA I 2016]

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Question : 19 of 26

Marks: +1, -0

What is the distance between the centre of the two circles ?

5 units
6 units
8 units
10 units

Solution:

Given equation o f circles

(x-1)^{2}+(y-3)^{2}=r^{2}

(h_{1},k_{1})\equiv

coordinates of centre

\equiv(1,3)

\therefore x^{2}+y^{2}-8x+2y+8=0

\Rightarrow (x-4)^{2}+(y+1)^{2}=(3)^{2}

(h_2,k_2)\equiv

coordinates o f centre

\equiv(4,-1)

Distance between centres of two circles

d=\sqrt{(h_{1}-h_{2})^{2}+(k_{1}-k_{2})^{2}}

\Rightarrow d=\sqrt{(1-4)^{2}+(3+1)^{2}}

\Rightarrow d=\sqrt{25}

d=5

units

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