JEE Main & Advanced
Sample Paper
JEE Main Sample Paper-21
question_answer
The equations of perpendicular bisectors of two sides AB and AC of a triangle ABC are \[x+y+1=0\]and \[x-y+1=0.\]respectively. If circumradius of \[\Delta \,ABC\] is 2 units and the locus of vertex A is \[{{x}^{2}}+{{y}^{2}}+gx+c=0,\]then \[({{g}^{2}}+{{c}^{2}}),\] is equal to
A) 4
B) 5
C) 9
D) 13
Correct Answer:
D
Solution :
The given lines intersect at (-1, 0) The vertex A lies on circle having centre at (-1, 0) and radius 2 units the vertex A lies on circle having centre at (-1, 0) and radius 2 units \[\Rightarrow \] Locus of A is \[{{(x+1)}^{2}}+{{y}^{2}}=4\] Hence g = 2 and c = -3 \[\Rightarrow \,\,{{g}^{2}}+{{c}^{2}}=13\]