A rod AB of the length 30 units slips on the coordinate axes such that A lies on x−axis and B lies on y−axis. Then, the locus of C if BC=2AC is
A
x2+4y2=400
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B
4x2+y2=400
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C
x2+4y2=100
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D
4x2+y2=100
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Solution
The correct option is Ax2+4y2=400 Let the points are A(a,0) and B(0,b) ∴√a2+b2=30⋯(1)
Let the coordinates of C is C(h,k) ∵C divides the rod AB into 2:1 ratio ∴h=2a3⇒a=3h2k=b3⇒b=3k
From (1) 9k2+9h24=302h2+4k2=400
locus of C is x2+4y2=400