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The tangent and the normal lines at the ...

The tangent and the normal lines at the point `1(sqrt3, 1)` to the circle `x^(2)+y^(2) = 4` and the X-axis form a triangle. The area of this triangle ( in square units ) is

A

`(1)/(3)`

B

`(4)/(sqrt3)`

C

`(2)/(sqrt3)`

D

`(1)/(sqrt3)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let T = 0 and N = 0 represents the tangent and normal lines at the point `P(sqrt3,1)` to the circle `x ^(2)+y^(2)=4`

So, equation of tangent (T=0) is
`sqrt3x+y = 4" "...(i)`
For point A , put y = 0, we get
`x=(4)/(sqrt3)`
`therefore " Area of requird " Delta OPA = (1)/(2) (OA)(PM)`
`=(1)/(2)xx(4)/(sqrt2)xx1`
`[therefore PM = "y-coordintate of P"]`
`=(2)/(sqrt3)` sq unit
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