# The system of equations |x| + |y| = 1  and  x2 + y2 = a2 will have ___ solutions if  1.  a=1 2.  1/2

pankaj kumar raman
51 Points
11 years ago

x sq. + y sq. = a sq.

means a circle of radious a unit

to lie on the circle., ιxι+ιyι=1 which is a square with extreme points (0,a),(a,0),(0,-a),(-a,0)

only these points will lie on the circle

hence there are 4 solutions for a=1

for a=1/2 no solutions because no point will intersect the square

Vikas TU
14149 Points
11 years ago

how do you find the coordinates?
and how we can say that its a square lying on the circle;

as it is looking like straight line eqn.

plz provide me the ansr properly.

pankaj kumar raman
51 Points
11 years ago

obviously we can say because ιxι cant be >1 and if ιxι is 1 then x can be either -1 or 1

hence y will be zero

see here all the points of ιxι+ιyι=1 satisfies the square formed and the inner circle doesnt intersect the square at any place

Roshan Mohanty
64 Points
10 years ago

|x| + |y| = 1 will have its corner points as (1,0) , (0,1) , (-1,0) , (0,-1) which is in the shape of a sqaure tilted by 45 degrees
x^2 + y+2 = a^2 is a circle with radius a units
1. a=1
so its graph of |x| + |y| =1 touches the circle at 4 above mentioned points by graph

2.a=1/2
raius is 1/2 unit
now the circle willlie inside the sqaure
so no solutions

plzz approve