Q.
The lines y=x+2 and y=x−22 are the tangents of certain circle. If the point (0,2) lies on the circle then it’s equation is
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a
(x−322)2+(y+122)2=94
b
(x+322)2+(y+122)2=94
c
(x−322)2+(y−122)2=94
d
None of the above
answer is C.
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Detailed Solution
Given lines are y=x+2........(1),y=x−22........(2) Diameter, d= distance between the two parallel lines (1)&(2)=|c1−c2|a2+b2=|2+22|2=3∴ radius, r=d2=32Let Q be the foot of the perpendicular from P with respect to line (2)h−x1a=k−y1b=−(ax1+by1+c)a2+b2⇒h−01=k−2−1=−(0−2−22)1+1h=k−2−1=322=32∴h=32,k=32+2=−12∴Q(h,k)=(32,−12)∴ Centre = midpoint of PQ=(32+02,−12+22)=(322,122)∴ Equation of the circle is (x−h)2+(y−k)2=r2⇒(x−322)2+(y−122)2=(32)2⇒(x−322)2+(y−122)2=94
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