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The Circle — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSThe Circle4 Marks
Question
One diameter of the circle circumscribing the rectangle ABCD is 4y = x + 7. If the coordinates of Aand B are (-3, 4) and (5, 4) respectively, find the equation of the circle.
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Answer

The centre O Ii es on the I ine x - 4y = -7 and the perpendicular bi sector MO of AB. The coordinates of Mare (1, 4). Thus, the equation of MO is x = 1 Point of intersection of x - 4y = -7 and x = 1 is 0 = (1, 2) Also the radius of ci rel e is $\text{AO}=\sqrt{(1+3)^2+(2-4)^2}$ $=\sqrt{16+4}=\sqrt{20}=2\sqrt{5}$ Thus the equation of circle is $(\text{x}-1)^2+(\text{y}-2)^2=20$ $\Rightarrow\text{x}^2+\text{y}^2-2\text{x}-4\text{y}-15=0$

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