Chapter 10: Conic Sections

Solution:

Since the axis is the x-axis, the equation is

y² = 4ax

Substitute point (2, 3):

3² = 4a × 2

9 = 8a

a = 9/8

Equation:

y² = 4 × (9/8)x

y² = (9/2)x

Multiplying by 2:

2y² = 9x

Answer: 2y² = 9x

Solution: 

A parabola symmetric about the y-axis has the equation:

x² = 4ay

Substitute point (5, 2):

25 = 4a × 2

25 = 8a

a = 25/8

Equation:

x² = 4 × (25/8)y

x² = (25/2)y

Multiplying by 2:

2x² = 25y

Answer: 2x² = 25y