Question

The equation of the parabola with vertex (-6,2), passing through (-3, 5) and having axis parallel to x-axis is

• A. (y+2)²=3x+16
• B. (x+6)²=3y-6
• C. (y+2)²=4x+48
• D. (x-6)²=4y-8
• E. (y-2)²=3x+18

Answer 1

Answer: (E)

Step 1: Identify the standard form of the parabola 
Since the axis of the parabola is parallel to the x-axis, the equation of the parabola is of the form: \[ (y - k)^2 = 4a (x - h) \] where \( (h, k) \) is the vertex. 
Given vertex: \( (-6,2) \), the equation becomes: \[ (y - 2)^2 = 4a (x + 6) \]

Step 2: Find the value of \( a \)  
The given point \( (-3,5) \) lies on the parabola. Substituting \( x = -3 \), \( y = 5 \) into the equation: \[ (5 - 2)^2 = 4a (-3 + 6) \] \[ 3^2 = 4a (3) \] \[ 9 = 12a \] \[ a = \frac{9}{12} = \frac{3}{4} \]

Step 3: Write the final equation 
Substituting \( a = \frac{3}{4} \): \[ (y - 2)^2 = 4 \times \frac{3}{4} (x + 6) \] \[ (y - 2)^2 = 3(x + 6) \] \[ (y - 2)^2 = 3x + 18 \]

Final Answer: The equation of the parabola is \((y - 2)^2 = 3x + 18\).