chetan2u wrote:

VyshakhR1995 wrote:

Does the line x + y = 6 intersect or touch the circle C with radius 5 units?

Center of the circle lies in the third quadrant.

Point (-4, -4) does not lie inside the circle.

Hi...

What does line x+y=6 mean when you draw it1) it lies in I, II and IV quadrant and not in III quadrant.

2) closest point to origin should be (3,3)

Let's see the statements..

I. Centre of circle is in III quadrant.

The closest point of line from origin is at (3,3) away..

Distance = \(\sqrt{3^2+3^2}=3\sqrt{2}\)..<5

The center can be taken just next to origin and the point (3,3) will be in the circle.

Also there will be infinite circles which are completely inside III quadrant and will not have any part of line in it.

Both yes and no possible

Insufficient

II. (-4,-4) does not lie in circle.

This point is 4√2 from centre and thus is more than the length of radius.

So a circle next to the origin as in statement I can have the line and not -4,-4.

Various combinations of circle exist where it will lie entirely in quadrant III.

Combined..

No new information

Insufficient

E

Hi

chetan2u I have a question.

Combining both statements, center of circle must be in third quadrant and (-4, -4) does not lie in the circle

Consider we are going to draw imaginary circle of radius (2 *5 = 10) with center at (-4, -4), and condition to draw is such that the mid-point of the radius lies the third quadrant, (actually the radius of this imaginary circle is diameter of the circle in the question), then we can see that we won't be able to complete drawing circle given (mid-point of radius should lie third quadrant) and this incomplete portion will have the line x+y = 6. Then it must be sufficient right?

actually i am not able to explain in words. if you draw a rough graph, line x+y = 6 and try to draw a circle with radius 10 and center (-4,4) and midpoint of radius must lie in third quadrant, then you can understand what i mean