# CAT 2019 Question Paper | Quants Slot 2

###### CAT Previous Year Paper | CAT Quants Questions | Question 3

Questions from the topic of Quadratic Equations can leave CAT aspirants in a jiffy and struggling to understand whether their CAT preparation online is going in the right direction. One good way to steer your online CAT Preparation is to solve CAT previous year paper questions. If you can ace these without having a look at the text and video solutions provided, you will be able to ace the questions that CAT exam throws at you as well. Do not procrastinate and leave it for another day! Solve this questions taken from CAT 2019 Question Paper right now! Make sure you do not look at the solution provided before attempting the question yourself!

Question 3 : Let a, b, x, y be real numbers such that a2 + b2 = 25 , x2 + y2 = 169 and ax + by = 65. If k = ay - bx, then

1. k = 0
2. k > $$frac{5}{13}$ 3. k = $\frac{5}{13}$ 4. 0 < k ≤ $\frac{5}{13}$ ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer Given equations are a2 + b2 = 25 and x2 + y2 = 169 We know 52 = 25 and 132 = 169 Multiply both equations to get$a2 + b2) (x2 + y2) = 25 x 169
(a2 + b2) (x2 + y2) = 6225
We know, 6225 = 652
We also know that ax + by = 65
So, numerically (Not algebraically), (a2 + b2) (x2 + y2) = (ax + by)2
(a2 + b2) (x2 + y2) = (ax + by)2
Expanding the equation,
a2 x2 + a2 y2 + b2 x2 + b2 y2 = a2 x2 + b2 y2 + 2axby
a2 y2 + b2 x2 = 2axby
a2 y2 + b2 x2 - 2axby = 0
This is of the form, (a-b)2
(ay-bx)2 = 0
ay - bx = 0
K = 0

The question is "Let a, b, x, y be real numbers such that a2 + b2 = 25 , x2 + y2 = 169 and ax + by = 65. If k = ay - bx, then "

##### Hence, the answer is k = 0

Choice A is the correct answer.

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