The equation of the parabola with focus (3, 0) and directrix x + 3 = 0 is
- y2=3x-9
- y2=4x-12
- y2=12x
- y2=12x-36
- y2=12x-9
The Correct Option is C
Solution and Explanation
Step 1: Find the vertex of the parabola
The vertex of a parabola is the midpoint between the focus and the directrix.
Given focus: \( (3,0) \)
Given directrix: \( x + 3 = 0 \Rightarrow x = -3 \)
The vertex is: \[ \left( \frac{3 + (-3)}{2}, \frac{0 + 0}{2} \right) = \left( \frac{0}{2}, 0 \right) = (0,0) \]
Step 2: Find the equation of the parabola
The standard equation of a parabola with vertex \( (h,k) \) and focus \( (h + a, k) \) (since it opens rightward) is: \[ (y - k)^2 = 4a (x - h) \] Here, \( h = 0 \), \( k = 0 \), and \( a = \) distance from vertex to focus: \[ a = 3 - 0 = 3 \] So, the equation becomes: \[ y^2 = 4(3)(x - 0) \] \[ y^2 = 12x \]
Final Answer: The equation of the parabola is \( y^2 = 12x \).
Top Questions on Parabola
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