Question

If A and S are respectively the vertex and focus of the parabola x² - 4x + 5y + 6 = 0, then the length of AS is

• A. $\frac{25}{16}$
• B. $\frac{\sqrt{13}}{4}$
• C. $\frac{5}{4}$
• D. $\frac{1}{2}$

Answer 1

Answer: (C)

$\frac{5}{4}$

Answer 2

AS = $\frac{1}{4}x$ latusrectum of the parabbola for the parabola λy = ax²+bx+c

Length of latusrectum = $\left| \frac{\lambda}{a} \right|$.

∴ Latusrectum of the parabola 5y = -x² + 4x – 6 is 5.

∴ AS = 5/4