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Question
Answer the following :
Find the equation of circle which passes through the origin and cuts of chords of length 4 and 6 on the positive side of x-axis and y-axis respectively
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Solution
Let the circle cut the chord of length 4 on X-axis at point A and the chord of length 6 on Y-axis at point B.
∴ the co-ordinates of point A are (4, 0) and co-ordinates of point B are (0, 6).
Since, ∠BOA is a right angle.
∴ AB represents the diameter of the circle
The equation of a circle having (x1, y1) and (x2, y2) as end points of diameter is given by
(x – x1) (x – x2) + (y – y1) (y – y2) = 0
Here, x1 = 4, y1 = 0, x2 = 0, y2 = 6
∴ the required equation of the circle is
(x – 4) (x – 0) + ( y – 0) (y – 6) = 0
∴ x2 – 4x + y2 – y = 0
∴ x2 + y2 – 4x – 6y = 0.
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