Question
Download Solution PDFFind the equation of the circle whose end points of the diameter are (- 3, 5) and (5, 3).
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
Let us suppose (x1, y1) and (x2, y2) be the end points of the diameter of a circle. Then the equation of such a circle is given by: (x – x1) ⋅ (x – x2) + (y – y1) (y – y2) = 0
CALCULATION:
Given: The points (- 3, 5) and (5, 3) are the end points of the diameter of the circle.
Here, we have to find the equation of the circle whose end points of the diameter are (- 3, 5) and (5, 3).
As we know that, if (x1, y1) and (x2, y2) be the end points of the diameter of a circle. Then the equation of such a circle is given by: (x – x1) ⋅ (x – x2) + (y – y1) (y – y2) = 0
Here, x1 = - 3, y1 = 5, x2 = 5 and y2 = 3
So, the equation of the required circle is: (x + 3) × (x – 5) + (y – 5) × (y – 3) = 0
⇒ x2 – 5x + 3x – 15 + y2 – 3y – 5y + 15 = 0
⇒ x2 – 2x – 15 + y2 – 8y + 15 = 0
⇒ x2 + y2 – 2x – 8y = 0
So, the equation of the circle is x2 + y2 – 2x – 8y = 0
Last updated on May 31, 2025
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