Question
Download Solution PDFFind the equation of a circle, if the end points of the diameters are A (3, 2) and B (2, 5) ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
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, 2) and B (2, 5).
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 = 2, x2 = 2 and y2 = 5
⇒ (x - 3) ⋅ (x - 2) + (y - 2) ⋅ (y - 5) = 0
⇒ x2 + y2 - 5x - 7y + 16 = 0
So, the equation of the required circle is: x2 + y2 - 5x - 7y + 16 = 0
Hence, option C is the correct answer.
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