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
18.3k views
in Parabola by (51.9k points)
closed by

Find the coordinates of the focus and the vertex, the equations of the directrix and the axis, and length of the latus rectum of the parabola:

(i) y= 12x

(ii) y= 10x

(iii) 3y2 = 8x

1 Answer

+1 vote
by (50.8k points)
selected by
 
Best answer

The general form of a parabola: y2 = 4ax ….(1)

Focus : F(a,0)

Vertex : A(0,0) (at any point A)

Equation of the directrix : x + a = 0

Axis: y = 0

Length of latus rectum : 4a

(i) y= 12x

On comparing given equation with (1), we have

4a = 12 => a = 3

Now,

Focus : F(a,0) = F(3,0)

Vertex : A(0,0)

Equation of the directrix : x + a = 0

=> x + 3 = 0

or x = -3

Axis: y = 0

Length of latus rectum : 4a = 4 x 3 = 12 units

(ii) y= 10x

On comparing given equation with (1), we have

4a = 10 => a = 2.5

Now,

Focus : F(a,0) = F(2.5,0)

Vertex : A(0,0)

Equation of the directrix : x + a = 0

=> x + 2.5 = 0

or x = -2.5

Axis: y = 0

Length of latus rectum : 4a = 4 x (2.5) = 10 units

(iii) 3y2 = 8x

or y2 = 8/3 x

On comparing given equation with (1), we have

4a = 8/3 => a = 2/3

Now,

Focus : F(a,0) = F(2/3,0)

Vertex : A(0,0)

Equation of the directrix : x + a = 0

=> x + 2/3 = 0

or x = -2/3

Axis: y = 0

Length of latus rectum : 4a = 4 x 2/3 = 8/3 units

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

...