What is the distance between the centres of the two circles ........

Mathematics (NDA) Coordinate Geometry

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Directions (2 Questions)
Consider the two circles (x − 1)² + ( y − 3)² = r ² and x² +y²− 8x + 2y + 8 = 0

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

5 units

6 units

8 units

10 units

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Explanation:

Given circle are
(x − 1)² + ( y − 3)² = r ² ...(i)
andx² +y²− 8x + 2y + 8 = 0 ...(ii)
Centre of circle (i) = (1, 3) and radius r₁ =r
Centre of circle (ii) = (4, − 1)
and radius (r ) ₂ = $\sqrt{16+1-8}$ = 3
$\therefore$ Distance between centres = $\sqrt{(1-4)^{2}+(3+1)^{2}}=\sqrt{25}=5$
= 5 units