Question: Find the equation of a circle whose centre is (-3,-4) and touches the X-axis.

Solution:

In a circle,
Coordinates of the Centre (h,k) = (-3,-4)
Passing point lies on the X-axis.

We know,
When a circle touches x-axis, its radius (r) = |k| units.
or, r = |k| units
or, r = |-4|
So, r = 4 units

Now,
Using formula for circle equation, we get,
(x - h)² + (y - k)² = r²

or, {x - (-3)}² + {y - (-4)}² = 4²

or, (x +3)² + (y +4)² = 16

or, (x² + 6x + 9) + (y² + 8y + 16) = 16

or, x² + y² + 6x + 8y + 9 = 0 is the required equation.

Hence, the required equation of the circle is x²+ y²+ 6x +8y +9 = 0.

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