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If the intercepts of the variable circle...

If the intercepts of the variable circle on the x- and yl-axis are 2 units and 4 units, respectively, then find the locus of the center of the variable circle.

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To find the locus of the center of a variable circle with given intercepts on the axes, we can follow these steps: ### Step 1: Understand the intercepts The problem states that the x-intercept of the circle is 2 units and the y-intercept is 4 units. This means that the circle intersects the x-axis at (2, 0) and the y-axis at (0, 4). ### Step 2: Use the formula for intercepts The length of the intercept on the x-axis can be expressed as: \[ ...
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