Q.

Through point P−1,4, two perpendicular lines are drawn which intersect x-axis at Q and R. Find the locus of incentre of ΔPQR.

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a

x2+y2+2x−8y−17=0

b

x2−y2+2x−8y+17=0

c

x2+y2−2x−8y−17=0

d

x2−y2+8x−2y−17=0

answer is B.

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Detailed Solution

Let Ih,k be incentre.Incentre is equidistant from all sides.By geometry, IP=k2∴   h+12+k−42=k2∴  h2+1+2h+k2+16−8k=2k2∴  h2−k2+2h−8k+17=0Hence, locus is x2−y2+2x−8y+17=0
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