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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