Q60 / 150 · MHT CET 2026 (13 April Shift 2) · Mathematics
The distance of the focus of the parabola $y^2 = 16x$ from its directrix is...
- A$4$
- Correct answerB$8$
- C$12$
- D$16$
Solution
The given equation of the parabola is $y^2 = 16x$.
Comparing this with the standard form $y^2 = 4ax$, we get $4a = 16$, which gives $a = 4$.
The coordinates of the focus are $(a, 0) = (4, 0)$.
The equation of the directrix is $x = -a$, which is $x = -4$.
The distance between the focus and the directrix is the perpendicular distance from the point $(4, 0)$ to the line $x + 4 = 0$.
Distance $= |4 - (-4)| = 8$.
Alternatively, the distance from the focus to the directrix for a parabola $y^2 = 4ax$ is always $2a$.
Distance $= 2 \times 4 = 8$.
Answer: $8$
Comparing this with the standard form $y^2 = 4ax$, we get $4a = 16$, which gives $a = 4$.
The coordinates of the focus are $(a, 0) = (4, 0)$.
The equation of the directrix is $x = -a$, which is $x = -4$.
The distance between the focus and the directrix is the perpendicular distance from the point $(4, 0)$ to the line $x + 4 = 0$.
Distance $= |4 - (-4)| = 8$.
Alternatively, the distance from the focus to the directrix for a parabola $y^2 = 4ax$ is always $2a$.
Distance $= 2 \times 4 = 8$.
Answer: $8$
Hence, the correct answer is option: 'B'.