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Question

Angle between tangent x2+y2=20, drawn to circles from the point (6,2) is


A

π2

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B

π

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C

π4

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D

2π

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Solution

The correct option is A

π2


Explanation for the correct option:

Step 1. The equation of the tangent to the circle x2+y2=20 is y=mx±201+m2.

This tangent passes through the point 6,2

put x=6 and y=2

2=6m±201+m2

2-6m=±201+m2

Step 2. Take square on Both sides.

2-6m2=2021+m2

2-6m2=201+m2 (a-b)2=a2+b2-2ab

4+36m2-24m=20+20m2

4+36m2-24m-20-20m2=0

-16+16m2-24m=0

16m2-24m-16=0

Step 3. Divide above equation by 8.

2m2-3m-2=0

2m2-4m+1m-2=0

2mm-2+1m-2=0

2m+1m-2=0

2m+1=0

2m=-1

m=-12

and m-2=0

m=2

m1=2 and m2=-12

Step 4. Required angle=tan-1m1+m21+m1m2

=tan-12-121+2-12=tan-14-122-42=tan-13×2-2×2=tan-1-32=tan-1=π2

Hence, option(A) is correct


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