Which of the following is NOT a point on the circle of radius 5 and

Question

https://gmatclub.com/forum/download/file.php?id=45129 Which of the following is NOT a point on the circle of radius 5 and center O as graphed above? (A) (-1, 2) (B) (8, -1) (C) (0, -5) (D) (6, 3) (E) (7, -6) CGEO.jpg

AnisMURR · Answer

We have to calculate the distance between O and each of the points.

We search for the one that is different than 5, because we want the point to be outside the circle.

The first 4 points lies on the circle, the last one NO.

So  Answer E

BrentGMATPrepNow · Answer

Time-killer alert! This is one of those questions that require us to check/test each answer choice. In these situations, always check the answer choices from E to A , because the correct answer is typically closer to the bottom than the top. For more on this strategy, see my article: https://www.gmatprepnow.com/articles/han ... -questions Cheers, Brent

Mo2men · Answer

The general formula of a circle:

(x-h)^2 + (y-k)^2 = r^2  ....where h & k are coordinates of the origin.

Using center above:

(x-3)^2 + (y+1)^2 = 5^2

Apply as Brent says above:

(E) (7, -6).......(7-3)^2 + (-6+1)^2 = 16 + 25 = 31.........So it does NOT belong to the circle

Answer: E

fskilnik · Answer

Let´s translate the x axis 1 unit down ("y" goes "y+1") and the y axis 3 units to the right ("x" goes "x-3")

Doing so, the center of the circle given is now at the origin(!) and "extremal points" are re-coordenated as shown:

https://preview.ibb.co/nJpfUq/22-Nov18-3z.gif

(A) (-1,2) goes to (-4,3)
(B) (8,-1) goes to (5, 0)
(C) (0,-5) goes to (-3, -4)
(D) (6,3) goes to (3,4)
(E) (7, -6) goes to  (4, -5)

It is clear that point  (4,-5)  does not belong to the given circle!

(It is also clear that all other points are on the circumference of the given circle... think about 3,4,5!)

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
Fabio.

ScottTargetTestPrep · Answer

Solution: 
 
The standard form of a circle with center (h, k) and radius r is (x - h)^2 + (y - k)^2 = r^2. Thus, we see that the equation of the given circle, with center (3, -1) and radius 5, will have the equation:

(x - 3)^2 + (y + 1)^2 = 25

If a point (a, b) is on circle O, then it will satisfy the above equation.

Of all the points given in the answer choices, (7, -6) is not on circle O since:

(7 - 3)^2 + (-6 + 1)^2 = 4^2 + (-5)^2 = 16 + 25 = 41 ≠ 25

Answer: E

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.

Which of the following is NOT a point on the circle of radius 5 and

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

Which of the following is NOT a point on the circle of radius 5 and

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