Question

if the coefficient ( a ) in the general quadratic equation is equal to 12, what is the focal length for the parabola, ( c ), equal to?
12
( \frac{1}{3} )
48
1
3
( \frac{1}{12} )
( \frac{1}{48} )

Explanation:

Step1: Recall the formula for focal length

The formula for the focal length \( c' \) of a parabola given by the quadratic equation \( y = ax^{2}+bx + c \) is \( c'=\frac{1}{4a} \).

Step2: Substitute \( a = 12 \) into the formula

Substitute \( a = 12 \) into \( c'=\frac{1}{4a} \). We get \( c'=\frac{1}{4\times12} \).

Step3: Calculate the value

Calculate \( \frac{1}{4\times12}=\frac{1}{48} \).

Answer:

\(\frac{1}{48}\) (the option \(\frac{1}{48}\))