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Question

Let the tangents from P are drawn to a circle with centre C such that PC=2 units. If equation of the tangents are x2=3y2, then radius of the circle can be
  1. 2 unit
  2. 3 unit
  3. 2 unit
  4. 1 unit


Solution

The correct options are
B 3 unit
D 1 unit
x2=3y2x=3y; x=3y
So P(0,0)
Now the centre of the required circle will lie on the angle bisector of the lines i.e., x=0; y=0
and it is given that PC=2 units

Now from above figure in PP1C1
C1PP1=30°
r=C1P1=PC1sin30°=1 unit

Now in PP2C2
C2PP2=60°
r=C2P2=PC2sin60°=3 unit

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