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Home » Find the centre and radius of each of the following circles: (i) (x – 1)2 + y2 = 4 (ii) (x + 5)2 + (y + 1)2 = 9
Find the centre and radius of each of the following circles: (i) (x – 1)2 + y2 = 4 (ii) (x + 5)2 + (y + 1)2 = 9
CBSE | Class 11 | Exercise 24.1 | Maths | RD Sharma | The Circle
Find the centre and radius of each of the following circles: (i) (x – 1)2 + y2 = 4 (ii) (x + 5)2 + (y + 1)2 = 9

    \[~{{\left( x\text{ }-\text{ }1 \right)}^{2}}~+\text{ }{{y}^{2}}~=\text{ }4\]

using the standard equation formula,

    \[{{\left( x\text{ }-\text{ }a \right)}^{2}}~+\text{ }{{\left( y\text{ }-\text{ }b \right)}^{2}}~=\text{ }{{r}^{2}}~\ldots .\text{ }\left( 1 \right)\]

Now let us convert given circle’s equation into the standard form.

    \[\begin{array}{*{35}{l}} {{\left( x\text{ }-\text{ }1 \right)}^{2}}~+\text{ }{{y}^{2}}~=\text{ }4 \\ {{\left( x\text{ }-\text{ }1 \right)}^{2}}~+\text{ }{{\left( y\text{ }-\text{ }0 \right)}^{2}}~=\text{ }{{2}^{2}}~\ldots ..\text{ }\left( 2 \right) \\ \end{array}\]

By comparing equation (2) with (1),

Centre = (1, 0) and radius = 2

∴ The centre of the circle is (1, 0) and the radius is 2.

(ii) 

    \[{{\left( x\text{ }+\text{ }5 \right)}^{2}}~+\text{ }{{\left( y\text{ }+\text{ }1 \right)}^{2}}~=\text{ }9\]

By using the standard equation formula,

    \[{{\left( x\text{ }-\text{ }a \right)}^{2}}~+\text{ }{{\left( y\text{ }-\text{ }b \right)}^{2}}~=\text{ }{{r}^{2}}~\ldots .\text{ }\left( 1 \right)\]

Now let us convert given circle’s equation into the standard form.

    \[\begin{array}{*{35}{l}} {{\left( x\text{ }+\text{ }5 \right)}^{2}}~+\text{ }{{\left( y\text{ }+\text{ }1 \right)}^{2}}~=\text{ }9 \\ {{\left( x\text{ }\text{ }-\left( -5 \right) \right)}^{2}}~+\text{ }{{\left( y\text{ }-\text{ }\left( \text{ }-\text{ }1 \right) \right)}^{2}}~=\text{ }{{3}^{2}}~\ldots .\text{ }\left( 2 \right) \\ \end{array}\]

By comparing equation (2) with (1), we get

Centre = (-5, -1) and radius = 3

∴ The centre of the circle is (-5, -1) and the radius is 3.

i

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