# Find the Centre and Radius of Each of the Following Circles: X2 + Y2 − 4x + 6y = 5 - Mathematics

Find the centre and radius of each of the following circles:

x2 + y2 − 4x + 6y = 5

#### Solution

Let (hk) be the centre of a circle with radius a.
Thus, its equation will be

$\left( x - h \right)^2 + \left( y - k \right)^2 = a^2$

Given:

$x^2 + y^2 - 4x + 6y = 5$

The given equation can be rewritten as follows:

$\left( x - 2 \right)^2 + \left( y + 3 \right)^2 - 4 - 9 = 5$
$\Rightarrow \left( x - 2 \right)^2 + \left( y + 3 \right)^2 = 18$
Thus, the centre is (2, −3).
And, radius = $\sqrt{18} = 3\sqrt{2}$
Concept: Circle - Standard Equation of a Circle
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 24 The circle
Exercise 24.1 | Q 2.3 | Page 21