AB is a chord of `x^2 + y^2 = 4` and P(1, 1) trisects AB. Then the length of the chord AB is (a) 1.5 units (c) 2.5 units (b) 2 units (d) 3 units

Options

A. 1.5 units
B. 2 units
C. 2.5 units
D. 3 units

Answer

D

Explanation

Given in `AP: AB = 2:1`
Let `AP = 2r` and `BP = r`
Using parametric equations
`A = (1-2r cos theta, 1 -2rsin theta)`
`B =(1+r cos theta, 1 +r sintheta)`
A lies on the circle `x^(2)+y^(2) =4`
`rArr (1-2r cos theta)^(2) + (1-2r sin theta)^(2) =4` (1)
B lies on the circle `x^(2)+y^(2) =4`
`rArr (1+r cos theta)^(2) + (1+r sin theta)^(2) =4` (2)
Solving (1) and (2), we get `r =1`
`rArr AB = sqrt((3r cos theta)^(2)+(3r sin theta)^(2)) =3r =3`