Equation of Family of Circles Touching a Line and Passing through a Given Point on the Line
If a circle S...
Question
If a circle S(x,y)=0 touches the line x + y = 5 at the point (2, 3) and S(1, 2) = 0, then the radius of such circle is .
A
r=32units
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B
r=12units
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C
r=3√2units
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D
r=1√2units
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Solution
The correct option is Dr=1√2units theequationoffamilyofcirclestouchingthelinex+y−5=0at(2,3)is(x−2)2+(y−3)2+λ(x+y−5)=0Also,(1,2)liesonit⇒1+1+λ(−2)=0⇒λ=1So,equationofrequiredcircleis:x2+y2−3x−5y+8=0Onsolving,weget:Radius=1√2units