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The centres of those circles which touch...

The centres of those circles which touch the circle, `x^2+y^2-8x-8y-4=0` , externally and also touch the x-axis, lie on : (1) a circle. (2) an ellipse which is not a circle. (3) a hyperbola. (4) a parabola.

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To solve the problem, we need to find the centers of circles that touch the given circle externally and also touch the x-axis. We will follow these steps: ### Step 1: Identify the given circle's equation The equation of the given circle is: \[ x^2 + y^2 - 8x - 8y - 4 = 0 \] ### Step 2: Rewrite the circle's equation in standard form To convert the equation into standard form, we complete the square for both \(x\) and \(y\). ...
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