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Question

A rod AB of the length 30 units slips on the coordinate axes such that A lies on xaxis and B lies on yaxis. 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 A x2+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=2a3a=3h2k=b3b=3k
From (1)
9k2+9h24=302h2+4k2=400
locus of C is
x2+4y2=400

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