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Find the equation of a circle, if the end points of the diameters are A (p, q) and B (r, s) ?

Find the equation of a circle, if the end points of the diameters are A (p, q) and B (r, s) ? Correct Answer (x - p) ⋅ (x - r) + (y - q) ⋅ (y - s) = 0

CONCEPT:

If (x1, y1) and (x2, y2) are the end points of the diameter of a circle. Then the equation of such a circle is (x – x1) ⋅ (x – x2) + (y – y1) (y – y2) = 0

CALCULATION:

Given: The end points of the diameter of a circle are A (p, q) and B (r, s)

As we know that, if (x1, y1) and (x2, y2) are the end points of the diameter of a circle then the equation of such a circle is (x – x1) ⋅ (x – x2) + (y – y1) (y – y2) = 0

Here, x1 = p, y1 = q, x2 = r and y2 = s.

⇒ (x - p) ⋅ (x - r) + (y - q) ⋅ (y - s) = 0

So, the equation of the required circle is: (x - p) ⋅ (x - r) + (y - q) ⋅ (y - s) = 0

Hence, option A is the correct answer.

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