Q.

If I1,I2,I3 are the intercept on x-axis, y-axis, y = x w.r.t. x2+y2−14x−10y+24=0   then

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a

I2>I3>I1

b

I3>I1>I2

c

I1>I3>I2

d

I3>I2>I1

answer is B.

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Detailed Solution

Given circle Is x2+y2−14x−10y+24=0 ⇒g=−7, f=−5, c=24Centre (−g,−f)=(7,5) ; r=49+25−24=52I1= x-intercept=2g2−c=249−24=10I2= y-intercept=2f2−c=225−24=2d=perpendicular distance from C(7,5) to x−y=0=|7−5|2=2Intercept on a line is chord of the circleI3= length 2r2−d2=250−2=83∴I3>I1>I2
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If I1,I2,I3 are the intercept on x-axis, y-axis, y = x w.r.t. x2+y2−14x−10y+24=0   then