Find the equation of the parabola with focus at \( (3,1) \) and vertex at \( (5,1) \).
Show Hint
- \( (y - 1)^2 = -8(x - 5) \)
- \( (y - 1)^2 = 8(x - 5) \)
- \( (y - 1)^2 = 8(x - 3) \)
- \( (y - 1)^2 = -8(x - 3) \)
- \( (y - 1)^2 = -4(x - 5) \)
The Correct Option is A
Solution and Explanation
The equation of a horizontal parabola is: \[ (y - k)^2 = 4p(x - h) \] where \( (h, k) \) is the vertex, and \( p \) is the distance from the vertex to the focus. Given: \[ (h, k) = (5,1), \quad (f_x, f_y) = (3,1) \] \[ p = f_x - h = 3 - 5 = -2 \] Substituting into the equation: \[ (y - 1)^2 = 4(-2)(x - 5) \] \[ (y - 1)^2 = -8(x - 5) \] Thus, the correct answer is:
Final Answer: \[ \boxed{(y - 1)^2 = -8(x - 5)} \]
Top Questions on Parabola
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