Question

What is the shape of the figure given by the following equations?

• A. \(16x^2 - 9y^2 - 64x - 54y - 161 = 0\)
• B. Line
• C. Ellipse
• D. Hyperbola

Answer 1

The Correct Option is A

All equations resemble conic sections but checking the difference between them: \[ \text{(i)} - \text{(iii)} \Rightarrow \text{Difference gives a linear expression}
\text{Similarly, combining and eliminating quadratic terms among (i), (ii), and (iii)} leads to linear dependencies, hence they represent the same line. \]