Discussion
Consider the function \(f(x, y) = \dfrac{x^{2}}{2} + \dfrac{y^{2}}{3} - 5\). All the roots of this function
Answer: B
The roots lie on an elliptical curve.
The roots are the points where \(f(x, y) = 0\):
\[ \begin{aligned} \frac{x^{2}}{2} + \frac{y^{2}}{3} &= 5 \\ \frac{x^{2}}{10} + \frac{y^{2}}{15} &= 1 \end{aligned} \]
This is an ellipse in the xy-plane with semi-axes \(\sqrt{10}\) along x and \(\sqrt{15}\) along y.
An ellipse has infinitely many points, so the roots are not a finite set. A sphere would need three variables, and the function has only two. A hyperbola would need the two squared terms to have opposite signs, but both are positive here.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development