Your cart is empty.
Practice each question, then open the answer or worked solution.
Find the coordinates of the focus, axis of the parabola, equation of the directrix and length of the latus rectum.
Given: y² = 12x
Solution: Compare the given equation with the standard form:
y² = 4ax
So,
4a = 12
a = 3
Now,
Focus = (a, 0) = (3, 0)
Axis = x-axis (y = 0)
Directrix = x = –a = x = –3
Length of latus rectum = 4a = 12
Answer:
Focus: (3, 0)
Axis: x-axis
Directrix: x = –3
Length of latus rectum: 12 units
Given: x² = 6y
Solution:
Compare with:
x² = 4ay
4a = 6
a = 3/2
Therefore,
Focus = (0, 3/2)
Axis = y-axis
Directrix = y = –3/2
Length of latus rectum = 6
Answer:
Focus: (0, 3/2)
Axis: y-axis
Directrix: y = –3/2
Length of latus rectum: 6 units
Given: y² = –8x
Solution:
Compare with:
y² = –4ax
4a = 8
a = 2
Hence,
Focus = (–2, 0)
Axis = x-axis
Directrix = x = 2
Length of latus rectum = 8
Answer:
Focus: (–2, 0)
Axis: x-axis
Directrix: x = 2
Length of latus rectum: 8 units
Given: x² = –16y
Solution:
Compare with:
x² = –4ay
4a = 16
a = 4
Therefore,
Focus = (0, –4)
Axis = y-axis
Directrix = y = 4
Length of latus rectum = 16
Answer:
Focus: (0, –4)
Axis: y-axis
Directrix: y = 4
Length of latus rectum: 16 units
Given: y² = 10x
Solution:
Compare with:
y² = 4ax
4a = 10
a = 5/2
Thus,
Focus = (5/2, 0)
Axis = x-axis
Directrix = x = –5/2
Length of latus rectum = 10
Answer:
Focus: (5/2, 0)
Axis: x-axis
Directrix: x = –5/2
Length of latus rectum: 10 units
Given: x² = –9y
Solution:
Compare with:
x² = –4ay
4a = 9
a = 9/4
Hence,
Focus = (0, –9/4)
Axis = y-axis
Directrix = y = 9/4
Length of latus rectum = 9
Answer:
Focus: (0, –9/4)
Axis: y-axis
Directrix: y = 9/4
Length of latus rectum: 9 units
Find the equation of the parabola whose focus is (6, 0) and directrix is x = –6.
Solution:
For a parabola opening rightward,
Focus = (a, 0)
Directrix = x = –a
Comparing,
a = 6
Using the standard equation:
y² = 4ax
y² = 4 × 6 × x
y² = 24x
Answer: y² = 24x
Find the equation of the parabola whose focus is (0, –3) and directrix is y = 3.
Solution:
The parabola opens downward.
Compare with:
Focus = (0, –a)
Directrix = y = a
Therefore,
a = 3
Standard equation:
x² = –4ay
x² = –12y
Answer: x² = –12y
Find the equation of the parabola whose vertex is (0, 0) and focus is (3, 0).
Solution:
Focus = (a, 0)
Therefore,
a = 3
Equation:
y² = 4ax
y² = 12x
Answer: y² = 12x
Find the equation of the parabola whose vertex is (0, 0) and focus is (–2, 0).
Solution:
Focus = (–a, 0)
a = 2
Equation:
y² = –4ax
y² = –8x
Answer: y² = –8x