Question

The directrix of the parabola \(y^2 + 4x + 3 = 0\) is

• A. \(x-\frac{4}{3}=0\)
• B. \(x+\frac{1}{4}=0\)
• C. \(x-\frac{3}{4}=0\)
• D. \(x-\frac{1}{4}=0\)

Hint:

For \(y^2=-4a(x-h)\), directrix is \(x=h+a\) and focus is \((h-a,0)\).

Answer 1

The Correct Option is D

Step 1: Rewrite parabola in standard form.
Given:
\[ y^2 + 4x + 3 = 0 \Rightarrow y^2 = -4x - 3 \Rightarrow y^2 = -4\left(x+\frac{3}{4}\right) \]
Step 2: Compare with standard equation.
Standard form:
\[ y^2 = -4a(x-h) \]
Here \(h = -\frac{3}{4}\) and \(a = 1\).
Step 3: Directrix formula.
For \(y^2 = -4a(x-h)\), directrix is:
\[ x = h + a \]
Step 4: Substitute values.
\[ x = -\frac{3}{4} + 1 = \frac{1}{4} \]
So directrix is:
\[ x-\frac{1}{4}=0 \]
Final Answer:
\[ \boxed{x-\frac{1}{4}=0} \]