SATHEE: Straight Line Question 232

Straight Line Question 232

Question: The equation $ {{(x^{2}-a^{2})}^{2}}{{(x^{2}-b^{2})}^{2}}+c^{4}{{(y^{2}-a^{2})}^{2}}=0 $ represents $ (c\ne 0) $

Options:

A) 8 points

B) Two circles

C) 4 lines

D) None of these

Show Answer

Answer:

Correct Answer: A

Solution:

[a] $ {{(x^{2}-a^{2})}^{2}}{{(x^{2}-b^{2})}^{2}}+c^{4}{{(y^{2}-a^{2})}^{2}}=0 $ This being the sum of two perfect squares, each term must be zero. Hence, we get $ {{(x^{2}-a^{2})}^{2}}{{(x^{2}-b^{2})}^{2}}=0 $ or $ (x^{2}-a^{2})(x^{2}-b^{2})=0 $ or $ (x-a)(x+a)(x-b)(x+b)=0 $ ? (1) and $ c^{4}{{(y^{2}-a^{2})}^{2}}=0 $ or $ c^{2}(y^{2}-a^{2})=0 $ or $ c^{2}(y+a)(y-a)=0 $ ? (2) Equation no. (1) Holds good for $ x=\pm a $ or $ x=\pm b $ Equation no. (2) Is satisfied by $ y=\pm a $ As both of these should be simultaneously satisfied, the give equation represents 8 points which we get as a result of different combinations of (1) and (2), namely $ (\pm a,\pm a),(\pm b,\pm a). $

BETA

sathee@iitk.ac.in

Media coverage of SATHEE

Play Store

App Store

The Ministry of Education has launched the SATHEE initiative in association with IIT Kanpur to provide free guidance for competitive exams. SATHEE offers a range of resources, including reference video lectures, mock tests, and other resources to support your preparation. Please note that participation in the SATHEE program does not guarantee clearing any exam or admission to any institute.

Ask SATHEE

Welcome to SATHEE !
Select from 'Menu' to explore our services, or ask SATHEE to get started. Let's embark on this journey of growth together! 🌐📚🚀🎓

I'm relatively new and can sometimes make mistakes.
If you notice any error, such as an incorrect solution, please use the thumbs down icon to aid my learning.
To begin your journey now, click on I understand

Please select your preferred language
कृपया अपनी पसंदीदा भाषा चुनें

Straight Line Question 232

Question: The equation $ {{(x^{2}-a^{2})}^{2}}{{(x^{2}-b^{2})}^{2}}+c^{4}{{(y^{2}-a^{2})}^{2}}=0 $ represents $ (c\ne 0) $

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Mentorship

NCERT Video Solution

Menu