Question

The axis of a parabola is parallel to Y-axis. If this parabola passes through the points \( (1,0), (0,2), (-1,-1) \) and its equation is \( ax^2 + bx + cy + d = 0 \), then \( \frac{ad}{bc} \) is:

• A. \(\frac{5}{8}\)
• B. \(\frac{5}{2}\)
• C. -10
• D. 10

Hint:

- Utilize symmetry and properties of parabolas aligned with coordinate axes to simplify calculations.

Answer 1

The Correct Option is D

- Substituting points into the general equation gives a system of linear equations in terms of \(a\), \(b\), \(c\), and \(d\). 
- Solve these equations to express \( a, b, c, \) and \( d \) in terms of each other. 
- Use Cramer's rule or matrix methods to find \( ad \) and \( bc \). 
- Calculate \( \frac{ad}{bc} \) from the solved values.