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Find the equation of a circle, the end points of one of whose diameters are A (3, 4) and B (5, 8) ?

Find the equation of a circle, the end points of one of whose diameters are A (3, 4) and B (5, 8) ? Correct Answer None of these

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 (3, 4) and B (5, 8).

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 = 3, y1 = 4, x2 = 5 and y2 = 8

⇒ (x - 3) ⋅ (x - 5) + (y - 4) ⋅ (y - 8) = 0

⇒ x2 + y2 - 8x - 12y + 47 = 0

So, the equation of the required circle is: x2 + y2 - 8x - 12y + 47 = 0

Hence, option D is the correct answer.

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