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The Sides of a Square Are X = 6, X = 9, Y = 3 and Y = 6. Find the Equation of a Circle Drawn on the Diagonal of the Square as Its Diameter.

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प्रश्न

The sides of a square are x = 6, x = 9, y = 3 and y = 6. Find the equation of a circle drawn on the diagonal of the square as its diameter.

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उत्तर

According to the question:
Sides of the square are x = 6, x = 9, y = 3 and y = 6.
The vertices of the square are (6, 6), (9, 6), (9, 3) and (6, 3).
And, the vertices of two diagonals are (6, 6), (9, 3) and (9, 6), (6, 3).
Hence, the equation of the circle is \[\left( x - 6 \right)\left( x - 9 \right) + \left( y - 6 \right)\left( y - 3 \right)\] or

\[x^2 + y^2 - 15x - 9y + 72 = 0\]
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Advanced Concept of Circle - Standard Equation of a Circle
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अध्याय 24: The circle - Exercise 24.3 [पृष्ठ ३७]

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आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 24 The circle
Exercise 24.3 | Q 3 | पृष्ठ ३७

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