Question:
If $(-3, 0)$ is the vertex and y-axis is the directrix of a parabola, then its focus is at the point:
If $(-3, 0)$ is the vertex and y-axis is the directrix of a parabola, then its focus is at the point:
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For horizontal parabola:
Vertex \( (h,k) \), focus is \( (h \pm a, k) \).
Direction depends on position of directrix.
Updated On: May 2, 2026
- $(0, -6)$
- $(-6, 0)$
- $(6, 0)$
- $(0, 0)$
- $(3, 0)$
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The Correct Option is B
Solution and Explanation
Concept:
For a parabola, the vertex lies midway between the focus and the directrix.
Distance from vertex to focus = distance from vertex to directrix = \( a \).
Step 1: Find the distance \( a \).
Directrix: \( x = 0 \), Vertex: \( (-3, 0) \) \[ a = \text{distance between vertex and directrix} = |-3 - 0| = 3 \]
Step 2: Determine direction of parabola.
Vertex is at \( x = -3 \) and directrix at \( x = 0 \) (to the right). Hence, parabola opens towards left, so focus lies to the left of vertex.
Step 3: Find coordinates of focus.
Move \( a = 3 \) units left from vertex: \[ (-3 - 3, 0) = (-6, 0) \]
Step 4: Final answer.
\[ \boxed{(-6, 0)} \]
Step 1: Find the distance \( a \).
Directrix: \( x = 0 \), Vertex: \( (-3, 0) \) \[ a = \text{distance between vertex and directrix} = |-3 - 0| = 3 \]
Step 2: Determine direction of parabola.
Vertex is at \( x = -3 \) and directrix at \( x = 0 \) (to the right). Hence, parabola opens towards left, so focus lies to the left of vertex.
Step 3: Find coordinates of focus.
Move \( a = 3 \) units left from vertex: \[ (-3 - 3, 0) = (-6, 0) \]
Step 4: Final answer.
\[ \boxed{(-6, 0)} \]
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