Question

The equation $16x^2+y^2+8xy-74x-78y+212=0$ represents

• A. a circle
• B. a parabola
• C. an ellipse
• D. hyperbola

Hint:

If $h^2-ab=0$ it's a parabola; if $<0$ it's an ellipse; if $>0$ it's a hyperbola.

Answer 1

The Correct Option is B

Step 1: Concept Identify the conic section using the discriminant $h^2 - ab$ from the general second-degree equation $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$.

Step 2: Meaning Here, $a=16$, $b=1$, and $2h=8 \implies h=4$.

Step 3: Analysis Calculate the discriminant: $h^2 - ab = (4)^2 - (16)(1) = 16 - 16 = 0$.

Step 4: Conclusion Since $h^2 - ab = 0$, the equation represents a parabola. Final Answer: (B)