Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Nov 2211:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Nov 23
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Nov 2510:00 AM EST
-11:00 AM EST
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.
05 May 2020, 04:14
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
59% (02:27) correct
41%
(02:14)
wrong
based on 172
sessions
History
Date
Time
Result
Not Attempted Yet
What is the area of the region enclosed by \(x^2 + y^2 + 6x + 8y ≤ 0\) and \(4x ≥ 3y\)?
A. \(\frac{25π}{4}\)
B. \(\frac{25π}{2}\)
C. \(25π\)
D. \(30π\)
E. \(35π\)
Are You Up For the Challenge: 700 Level Questions
A. \(\frac{25π}{4}\)
B. \(\frac{25π}{2}\)
C. \(25π\)
D. \(30π\)
E. \(35π\)
Are You Up For the Challenge: 700 Level Questions
28 May 2020, 11:03
Kudos
Bookmarks
nikitamaheshwari
Now i can see where you're getting confused
y≤ mx represents the region below the line y=mx (including points on the line).
y ≥ mx represents the region above the line y=mx (including points on the line).
So \(y≤ \frac{4x}{3}\) represents the region(in grey) below the line \(y=\frac{4x}{3}\) (in red).
Untitled.png [ 5.19 KiB | Viewed 6204 times ]
Also, \(x^2+y^2≤ r^2\) represents the region inside the circle (including points on the circle).
\(x^2+y^2 ≥ r^2\) represents the region outside the circle (including points on the circle).
So, \((x+3)^2+(y+4)^2 ≤ 5^2\) represents the region (in grey) inside the circle \((x+3)^2+(y+4)^2 = 5^2\) (in red)
Untitled 1.png [ 5.95 KiB | Viewed 6176 times ]
Now we have to find the common region (in grey), which is below the line y= 4x/3 and which is inside the circle.
Untitled.png [ 5.85 KiB | Viewed 6137 times ]
It's half of the area of the circle.
Now i can see where you're getting confused
y≤ mx represents the region below the line y=mx (including points on the line).
y ≥ mx represents the region above the line y=mx (including points on the line).
So \(y≤ \frac{4x}{3}\) represents the region(in grey) below the line \(y=\frac{4x}{3}\) (in red).
Attachment:
Untitled.png [ 5.19 KiB | Viewed 6204 times ]
Also, \(x^2+y^2≤ r^2\) represents the region inside the circle (including points on the circle).
\(x^2+y^2 ≥ r^2\) represents the region outside the circle (including points on the circle).
So, \((x+3)^2+(y+4)^2 ≤ 5^2\) represents the region (in grey) inside the circle \((x+3)^2+(y+4)^2 = 5^2\) (in red)
Attachment:
Untitled 1.png [ 5.95 KiB | Viewed 6176 times ]
Now we have to find the common region (in grey), which is below the line y= 4x/3 and which is inside the circle.
Attachment:
Untitled.png [ 5.85 KiB | Viewed 6137 times ]
It's half of the area of the circle.
General Discussion
05 May 2020, 17:28
Kudos
Bookmarks
\(x^2 + y^2 + 6x + 8y ≤ 0\)
\(x^2+6x+9-9 +y^2+8y+16-16≤ 0\)
\((x+3)^2 + (y+4)^2 ≤ 25\)
\((x+3)^2 + (y+4)^2 ≤ 5^2\)
This represents the region inside the circle whose coordinates of the center are (-3,-4) and whose radius is 5. (Red one)
\(4x ≥ 3y\) represents the region below the line 4x=3y(Blue one). Also, the line 4x=3y passes through the center of the circle, (-3,-4), so it cuts the circle in two equal parts. 
Capture.PNG [ 40.04 KiB | Viewed 6405 times ]
Area of the circle= π*5^2 = 25π
The area of the region enclosed by \(x^2 + y^2 + 6x + 8y ≤ 0\) and \(4x ≥ 3y\) =\( \frac{25π}{2}\)
\(x^2+6x+9-9 +y^2+8y+16-16≤ 0\)
\((x+3)^2 + (y+4)^2 ≤ 25\)
\((x+3)^2 + (y+4)^2 ≤ 5^2\)
This represents the region inside the circle whose coordinates of the center are (-3,-4) and whose radius is 5. (Red one)
\(4x ≥ 3y\) represents the region below the line 4x=3y(Blue one). Also, the line 4x=3y passes through the center of the circle, (-3,-4), so it cuts the circle in two equal parts.
Attachment:
Capture.PNG [ 40.04 KiB | Viewed 6405 times ]
Area of the circle= π*5^2 = 25π
The area of the region enclosed by \(x^2 + y^2 + 6x + 8y ≤ 0\) and \(4x ≥ 3y\) =\( \frac{25π}{2}\)
Bunuel
