=1 x+3y=3 x=(3−3y) Intersection point of line AP & circle is P(x0,y0) x2+y2=9⇒(3−3y)2+y2=9 ⇒32(1+y2−2y)+y2=9 ⇒5y2−9y=0⇒y(5y−9)=0 ⇒y=9∕5 Hence x=3(1−y)=3(1−
9
5
)=3(
−4
5
) x=
−12
5
P(x0,y0)=(
−12
5
,
9
5
) Area of △AOP is =
1
2
×OA× height Height =9∕5,OA=3 =
1
2
×3×
9
5
=
27
10
=
m
n
Compare both side m=27,n=10⇒m−n=17 Therefore, correct answer is option-D