Question

Find the coordinate of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.

1. y² = 20x

2. x² = 8

3. 3x² = -15

Answer 1

1. Comparing the equation with the general form we get; 

4a = 20 ⇒ a = 5

Coordinate of focus are (5, 0)

Axis of the parabola is y = 0

Equation of the directrix is x = -5

Length of latus rectum = 4 × 5 = 20.

2. Comparing the equation with the general form we get; 

4a = 8 ⇒ a = 2

Coordinate of focus are (0, 2)

Axis of the parabola is x = 0

Equation of the directrix is y = – 2

Length of latus rectum = 4 × 2 = 8.

3. Convert the equation into general form, we get x² = -5y. 

Comparing the equation with the general form we get;

4a = 5 ⇒ a = \(\frac{5}{4}\)

Coordinate of focus are (0, −\(\frac{5}{4}\))

Axis of the parabola is x = 0

Equation of the directrix is y = \(\frac{5}{4}\)

Length of latus rectum = \(\frac{4 \times 5}{4}\) = 5.