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Question

If the centre of the circle passing through the origin is (3, 4), then the intercepts cut off by the circle on x-axis and y-axis respectively are

A
3 unit and 4 unit
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B
6 unit and 4 unit
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C
3 unit and 8 unit
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D
6 unit and 8 unit
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Solution

The correct option is D 6 unit and 8 unit
Solution:
We have, Centre=(3,4) and radius =5
Equation of the required circle is
(x3)2+(y4)2=52
For x intercept,put y=0 we get
(x3)2+16=25
or, (x3)2=9
or, x3=±3
or, x=6 and x=0
Now,
For y intercept,put x=0 we get
9+(y4)2=25
or, (y4)2=16
or, y4=±4
or, y=8 and y=0
Hence, xintercept is 6 units and y intercept is 8 units.
Hence, D is the correct option.

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