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Question

The equations of the circle which pass through the origin and make intercepts of lengths 4 and 8 on the x and y - axes respectively are


A

x2+y2±4x±8y=0

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B

x2+y2±2x±4y=0

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C

x2+y2±8x±16y=0

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D

x2+y2±x±y=0

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Solution

The correct option is A

x2+y2±4x±8y=0


Estimate the Equation of the Circle:

Let S=x2+y2+2gx+2fy=0 be the equation of the circle which passes through the origin, C=-g,-f,r=g2+f2 .

Given that it makes intercept of 4 with x-axis 4=2r2-d2.

where d is distance between center and chord

C is the center of the circle,

g and f are coefficients used in the general equation of the circle.

2=g2+f2-f2g=±24=g2+f2-g2f=±4

So, the equation of circle is x2+y2±4x±8y=0.

Hence, the required equation is x2+y2±4x±8y=0 and therefore option A is correct.


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