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The Circle — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSThe Circle4 Marks
Question
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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Answer

Let the sides $A B, B C, C D$ and $D A$ of the square $A B C D$ be represented by the equations $y=3, x=6, y=6$ and $x=9$ respectively. Then, coordinates are $A(6,3), B(9,3), C(9,6)$ and $D(6,6)$. The equation of the circle with diagonal $A C(x-$ 6) $(x-9)+(4-3)(4-6)=0 \Rightarrow x^2-6 x-9 x+54+y^2-3 y-6 y+18=0 \Rightarrow x^2+y^2-15 x-9 y+72=0$ The equation of the circle with diagonal $B D$ as diameter is $(x-9)(x-6)+(y-3)(y-6)=\Rightarrow x^2-9 x-6 x+54+y^2-3 y-6 y+18=0 \Rightarrow$ $x^2+y^2-15 x-9 y+72=0 x^2+y^2-15 x-9 y+72=0$

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