gmatprep question on coordinate geo

[fak]

is a<2?

1) in the xyplane, the point (a,1) lies inside the circle whose equation is x^2 + y^2 = 3

2) in the xyplane, the point (a,4) lies on the line whose equation is 2x + 4y= 10


Statement 1 seems to a bit tricky, would some one please explain.
I have got the right answer but I want a more clear picture on this.

[mondegreen]

is a<2?

1) in the xyplane, the point (a,1) lies inside the circle whose equation is x^2 + y^2 = 3

2) in the xyplane, the point (a,4) lies on the line whose equation is 2x + 4y= 10


Statement 1 seems to a bit tricky, would some one please explain.
I have got the right answer but I want a more clear picture on this.

The radius of the circle from the first statement is 1.732 and the center at the origin(0,0)

Distance between any point ON the circle and the center : equals the radius.

Distance between any point INSIDE the circle and the center:
less than the radius

Distance between any point OUTSIDE the circle and the center:
more than the radius.

This line of thinking might help you with any doubts with the First Fact statement.

[fak]

but how do you know that circle has radius 1.7 ---
are you using the distance formula on this
can you please type out the steps you take to get root 3 as the radius.

why did you take origin to calculate the radius?

[mondegreen]

but how do you know that circle has radius 1.7 ---
are you using the distance formula on this
can you please type out the steps you take to get root 3 as the radius.

why did you take origin to calculate the radius?

Generic Equation of a circle:

(x-a)^2+(y-b)^2 = r^2.

The center for the circle will be (a,b) and the radius r.

Compare the generic equation to the given equation above.

And yes, the generic equation is nothing but distance formula applied to any point ON the circle.It is how a circle is defined.

[fak]

got it thanks

[RonPurewal]

The radius of the circle is √3, and the center is at the origin. So, the coordinates of any point inside the circle will be less than √3, which is less than 2.

[fak]

The radius of the circle is √3, and the center is at the origin. So, the coordinates of any point inside the circle will be less than √3, which is less than 2.

Thanks for the reply.

What I was doing wrong was replacing a in the equation that generated a square root and + , - value.

My approach was wrong m should've just approached it as told above

[RonPurewal]

Ok. Just get that as a takeaway for next time.