    Question

# The lengths of the intercepts made by any circle on the coordinates axes are equal if the centre lies on the line (s) represented by

A

x+y+1=0

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B

x+y=1

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C

x2y2=0

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D

x-y=1

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Solution

## The correct option is C x2−y2=0 Let the equation of any circle be x2+y2+2gx+2fy+c=0 (i) For intercept made by the circle on x-axis, put y=0 in (i) ⇒x2+2gx+c=0 (ii) If x1,x2 are roots of (ii), then length of the intercept on x-axis is |x1−x2|=√(x1+x2)2−4x1x2=2√g2−c Similarly, length of the intercept of the y-axis is 2√f2−c Since, the lengths of these intercepts are equal √g2−c=√f2−c ⇒g2=f2=(−g)2=(−f)2 Therefore, centre on x2−y2=0  Suggest Corrections  0      Similar questions
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