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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 - Mathematics and Statistics

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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

Sum
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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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Chapter 6: Circle - Miscellaneous Exercise 6 [Page 137]

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