# CAT Quantitative Aptitude Questions | Questions for CAT - Coordinate Geometry

###### CAT Questions | CAT Coordinate Geometry | Circle and chord
CAT Questions

The question is from CAT Coordinate Geometry. This is about area of a segment. We need to find out the area of intersecting region between a circle and a chord. Take Geometry, add one unit of algebra; take a diagram, explain it with x's and y's. For the purists, it is geometry without the romance, for the pragmatists it is Geometry with expanded scope. It is important to cover ideas from Coordinate Geometry in your CAT Preparation.

Question 6: Find the area of the region that comprises all points that satisfy the two conditions x2 + y2 + 6x + 8y ≤ 0 and 4x ≥ 3y?

1. 25π
2. 25$$frac{π}{4}\\$ 3. 25$\frac{π}{2}\\$ 4. None of these ## Rs. 2500 off on 2IIM Ultimate DI LR Course for CAT 2019. Offer valid till March 24th. #### Signup to sample the Best CAT Online Coaching ### Video Explanation ## Best CAT Coaching in Chennai #### Starts Sat, Mar 23, 2019 ### Explanatory Answer ##### Method of solving this CAT Question from CAT Coordinate Geometry: If a question looks very tough, perhaps there is some special factor that simplifies it. Perhaps a particular chord is actually a diameter? x2 + y2 + 6x + 8y < 0 x2 + 6x + 9 – 9 + y2 + 8y + 16 – 16 < 0$x + 3)2 + (y + 4)2 < 25

This represents a circular region with centre (–3, –4) and radius 5 units. Substituting x = y = 0, we also see that the inequation is satisfied. This means that the circle also passes through the origin. To find out the intercepts that the circle cuts off with the axes, substitute x = 0 to find out the y–intercept and y = 0 to find out x–intercept. Thus x–intercept = –6 and y–intercept = –8.

Now, the line 4x = 3y passes through the point (–3, –4). Or this line is the diameter of the circle. The area we are looking for is the area of a semicircle.
Required area = 25$$frac{π}{2}\\$ The question is "Find the area of the region that comprises all points that satisfy the two conditions x2 + y2 + 6x + 8y ≤ 0 and 4x ≥ 3y?" ##### Hence, the answer is 25$\frac{π}{2}\\$ sq units Choice C is the correct answer. ###### Online CAT CoachingTry it free! Register in 2 easy steps and start learning in 30 seconds! ###### Already have an Account? ###### CAT Coaching in Chennai Next Weekend Batch Starts Sat, Mar 23rd, 2019 ###### Best CAT Coaching in Chennai Sign up for a Free Demo of our CAT Coaching in Chennai ## CAT Preparation Online | CAT Geometry - Trigonometry Videos On YouTube #### Other useful sources for Geometry Questions | Coordinate Geometry Questions ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 10-C, Kalinga Colony, Bobbili Raja Salai K.K.Nagar, Chennai. India. Pin - 600 078 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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