Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
771 views
in Parabola by (48.7k points)
closed by
Find the equation of parabolas directrix x = 0, focus at (6, 0).

1 Answer

+1 vote
by (50.2k points)
selected by
 
Best answer

The distance of any point on the parabola from its focus and its directrix is same.

Given that, directrix, x = 0 and focus = (6, 0)

If a parabola has a vertical axis, the standard form of the equation of the parabola is (x - h)2 = 4p(y - k), where p≠ 0.

The vertex of this parabola is at (h, k).

The focus is at (h, k + p) & the directrix is the line y = k - p.

As the focus lies on x – axis,

Equation is y2 = 4ax or y2 = -4ax

So, for any point P(x, y) on the parabola

Distance of point from directrix = Distance of point from focus

x2 = (x – 6)2 + y2

x2 = x2 - 12x + 36 + y2

y2 - 12x + 36 = 0

Hence the required equation is y2 - 12x + 36 = 0.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...