Find the equation of the circle concentric with the circle ${x^2} + {y^2} - 4x - 6y - 3 = 0$ and which touches the y-axis.

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Find the equation of the circle concentric with the circle ${x^2} + {y^2} - 4x - 6y - 3 = 0$ and which touches the y-axis.

Answer:

The general equation of the circle is,

x² + y² + 2gx + 2fy + c = 0

Radius,

r =

$\begin{array}{l} r = \sqrt {{{(2)}^2} + {{(3)}^2} - ( - 3)} \\ r = \sqrt {4 + 9 + 3} \\ r = 4units \end{array}$

The equation of the circle which is concentric to the given circle and touches y-axis.

The centre of the circle remains the same and the y-axis will be tangent to the circle.

Point of contact will be (0, 3)

Radius = 2

Equation of the circle:

(x – 2)² + (y – 3)² = (2)²

x² + 4 – 4x + y² + 9 – 6y = 4

x² + y2 – 4x – 6y + 9 = 0

i

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