99 Percentile Qs Bank for JEE MainMathematicsStraight Lines

The four distinct points (0,0),(2,0),(0,-2) and (k,-2) are concyclic, if k is equal to

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Correct answer

D. 2

Step-by-step solution

Let the equation of the circle is aligned & x^2+y^2+2 g x+2 f y+c=0 & at (0,0), 0+0+0+0+c=0 c=0 & at (2,0), 4+0+2 g 2+0+0=0 & g=-1 & at (0,-2), 0+4+0-4 f+0=0 f=1 & at (k,-2), k^2+4+2 k g-4 f+0=0 & k^2+4-2 k-4=0 & k(k-2)=0 & k=0, k=2 & aligned

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