In the xy-plane, each point on circle K has nonnegative coordinates an

Question

In the xy-plane, each point on circle K has nonnegative coordinates and the center of K is the point (4, 7). What is the maximum possible area of K ?

A.  4\pi

B.  9\pi

C.  16\pi

D.  28\pi

E.  49\pi

This question is already posted in the forum. My doubt is why it cant be the 7. everybody is saying it could touch negative coordinates. please explain in detail

Bunuel · Accepted Answer

The circles with radius of 4 (blue) and 7 (red): Circle.png As you can see if the circle has the radius of 7 some of its points will be in II quadrant so will have negative x coordinate, but we are told that: "each point on the circle k has non negative coordinates ", so the radius of 7 is not possible (or any other radius more than 4). So, the max radius is 4, which makes the max area equal to \pi{r^2}=16\pi . Answer: C. Hope it's clear.

hsn81960 · Answer

hi, 
I still dont get this point :
As you can see if the circle has the radius of 7 some of its points will be in II quadrant so will have negative x coordinate?

How did u arrive to this conclusion?

saby1410 · Answer

VeritasKarishma   Bunuel

how to approach this question how you thought that we need radius as 4 or 7 to calculate area 
please help

siddhantvarma · Answer

The circle K has its center at (4, 7). The constraint that each point on the circle has nonnegative coordinates means that the circle can't extend into the negative x or y regions. The circle needs to be in the first quadrant of the plane only.

Area = πr²
To maximize the area, we need to find the largest possible radius that satisfies this constraint. So there can only be two scenarios, either the radius is 4 units or 7 units. Clearly, 7 units gives us the larger area but we need to check if it will extend to any other quadrant. A 7 units radius means from the center, we can go left 7 units along X axis. This will give us a point on the circle from the center. To get x the coordinate of this point, we'll go 7 units to the left = 4 - 7 => -3. This will give us a negative cooridnate.

Therefore, the maximum radius will be 4 units, the distance from the centre to the y-axis.

With a radius of 4, the area would be: A = π(4)² = 16πTherefore, the maximum possible area of K is 16π. (C)

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

In the xy-plane, each point on circle K has nonnegative coordinates an

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

In the xy-plane, each point on circle K has nonnegative coordinates an

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards