The area of the triangle formed by joining the origin to the point of intersection of the line `xsqrt(5)+2y=3sqrt(5)` and the circle `x^2+y^2 =10` is (a) 3 (b) 4 (c) 5 (d) 6

Options

A. 3
B. 4
C. 5
D. 6

Answer

3

Explanation

The length of perpendicular from the origin to the line `x sqrt(5)+2y=3 sqrt(5)` is
`OL=(3sqrt(5))/(sqrt((sqrt(5))^(2))+2^(2))=(3sqrt(5))/(sqrt(9))=sqrt(5)`
Radius of the given circle `sqrt(10)=OQ=OP`
`PQ=2QL=2sqrt(OQ^(2)-OL^(2))`
`2sqrt(10-5)=2sqrt(5)`
Thus, area of `Delta OPQ=(1)/(2)xx PQxxOL`
`(1)/(2)xx 2 sqrt(5) xxsqrt(5)=5`