Question
Download Solution PDFWhat is the equation of the circle whose diameter is 10 cm and the equations of two of its diameters are and ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
Given two diameters of the circle are along the lines x + y = 0 and x - y = 0. The center of the circle is at their intersection.
We have,
\(x - y = 0 \;\Longrightarrow\; x = y.\)
Substitute into x + y = 0:
\(x + x = 0 \;\Longrightarrow\; 2x = 0 \;\Longrightarrow\; x = 0,\; y = 0.\)
Thus, the center is (0, 0).
Also radius,
\(r = \frac{10}{2} = 5.\)
the equation of the circle with center (0,0) and radius 5 is
\(x^{2} + y^{2} = 5^{2} = 25.\)
Hence, the correct answer is Option 2.
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