A circle of radius 2 lies in the first quadrant and touches both the axis.Find the equation of the circle with the centre at (6,5) and touching the above circle externally.

Dear Student!

Let the centre of the given circle be (*h*, *k*).

The circle of radius 2 lies in the first quadrant and touches both the ares.

∴ *h* = *k* = 2

The equation of the given circle is

(*x* – 2)^{2} + (*y* – 2)^{2} = 2^{2}

⇒ (*x* – 2)^{2} + (*y* – 2)^{2} = 4 ...(1)

Let the radius of the required circle be *r.*

∴ The equation of the required circle is

(*x* – 6)^{2} + (*y* – 5)^{2} = *r*^{2} ...(2)

Given, circle (1) and (2) touch each other externally.

∴ Sum of their radius = Distance between their centres

∴ *r* = 5 – 2 = 3

Hence, the equations of the required circle is

(*x* – 6)^{2} + (*y* – 5)^{2} = 3^{2 } (Using(2))

⇒ (*x* – 6)^{2} + (*y* – 5)^{2} = 9

Cheers!

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