CAT Quantitative Aptitude Questions | Questions for CAT - Coordinate Geometry

CAT Questions | CAT Coordinate Geometry | Circle and chord

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

🎉 Flat ₹ 7,000 off on our CAT '24 & '25 Courses!
Valid till 31st Mar.


Register Now


Video Explanation


Best CAT Coaching in Chennai


CAT Coaching in Chennai - CAT 2022
Limited Seats Available - Register Now!


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.

CAT : Geometry: Coordinate Geometry Circle

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.

 


CAT Preparation Online | CAT Geometry - Trigonometry Videos On YouTube


Other useful sources for Geometry Questions | Coordinate Geometry Questions


CAT Questions | CAT Quantitative Aptitude

CAT Questions | CAT DILR

CAT Questions | Verbal Ability for CAT


Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093

How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now
Email: prep@2iim.com