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Find the Equation of the Circle Passing Through the Origin and the Points Where the Line 3x + 4y = 12 Meets the Axes of Coordinates. - Mathematics

Find the equation of the circle passing through the origin and the points where the line 3x + 4y = 12 meets the axes of coordinates.

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Solution

Putting x = 0 in 3x + 4y = 12:
y = 3
Putting y = 0 in 3x + 4y = 12:
x = 4
Thus, the line 3x + 4y = 12 meets the axes of coordinates at points A (0, 3) and B (4, 0).
The equation of the circle with AB as the diameter is

\[\left( x - 0 \right)\left( x - 4 \right) + \left( y - 3 \right)\left( y - 0 \right) = 0\] or \[x^2 - 4x + y^2 - 3y = 0\]
Hence, the required equation is
\[x^2 - 4x + y^2 - 3y = 0\]
Concept: Circle - Standard Equation of a Circle
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 24 The circle
Exercise 24.3 | Q 5 | Page 37
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