Question

Is a < 2 ?

(1) In the xy-plane, the point (a,1) lies inside the circle whose equation is x2 + y2 = 3.
(2) In the xy-plane, the point (a,4) lies on the line whose equation is 2y + 4x = 10.

Answer 1

yes to both

Explanation:

(1) For y=1, and x=a, ...

a² + 1² ≤ 3

-√2 ≤ a ≤ √2 . . . . . subtract 1 and take the square root

All values of "a" are less than 2 inside the circle.

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(2) For y=4 and x=a, ...

2·4 +4·a = 10

4a = 2 . . . . . . . subtract 8

a = 1/2 . . . . . . .divide by 4

The value of "a" for point (a, 4) on the line is less than 2.