Join Sarthaks eConnect Today - Largest Online Education Community!
0 votes
9 views
asked in Mathematics by (67.2k points)

Find the equation of axis, vertex, directrix, extremities of latus rectum and length of latus rectum of the parabola x2 – 3y + 2x + 3 = 0.

1 Answer

+1 vote
answered by (62.5k points)
selected by
 
Best answer

x2 –3y + 2x + 3 = 0

x2 + 2x + 1 = 3y – 2 ⇒ (x + 1)2 = 3(y -2/3).

Its axis is the line x + 1 = 0.

It's vertex is (-1, 2/3).

It's focus is  x + 1 = 0, y - 2/3 = 3/4 i.e., (-1, 17/12). 

It's directrix is the line y - 2/3 = - 3/4, i.e., y + 1/12 = 0.

It's  latus rectum is the line y - 2/3 = 3/4. i.e., y - 17/12 =  0.

Extremities of it,s latus rectum are x + 1 = 3/2, y - 2/3, i.e., (1/2, 17/12).

Length of it's latus rectum is 3 units.

Happy Diwali Wishes

Related questions

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.

One Thought Forever

“There is a close connection between getting up in the world and getting up in the morning.“
– Anon
~~~*****~~~

Categories

...