Find the focus and the directrix of the parabola y2 = 2a(x – 4a) and give the length of the latus rectum
Find the focus and the directrix of the parabola y2 = 2a(x – 4a) and give the length of the latus rectum
Samuel William , 6 Years ago
Grade 12
Analytical Geometry> Find the focus and the directrix of the p...
2 Answers
Aditya Gupta
eqn is y2 = 4(a/2)(x – 4a)= 4(a/2)X, where X= x – 4a
now obviously focus, directrix and latus rectum of y^2= 4bX are (b, 0), X= – b and 4b.
so, in our original coordinate system, focus is (4a + a/2, 0), directrix is x – 4a= – a/2 or x= 7a/2 and latus rectum= 4a/2 (as it is a length).
so, focus: (9a/2, 0)
directrix: 2x= 7a
LR= 2a
kindly approve :)
Sai Soumya
The required answer is according to the given equation is
FOCUS : (9a/2,0)
DIRECTRIX : X=7a/2
LENGTH OF LATUS RECTUM : 2a
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Other Related Questions on analytical geometry
- The locus of the point represented by x= t^2 +t+1 and y=t^-t+1 is
- The locus of the point represented by x= t^2 +t+1 and y=t^-t+1 is
analytical geometry
1 Answer Available
Last Activity: 3 Years ago
show that the centroids of the triangles of which three perpendiculars lie along the lines y=m1x,y=m2x,y=m3x lie on y(3+m2m3+m3m2+m1m2)=x(m1+m2+m3+3m1m2m3)
show that the centroids of the triangles of which three perpendiculars lie along the lines y=m1x,y=m2x,y=m3x lie on y(3+m2m3+m3m2+m1m2)=x(m1+m2+m3+3m1m2m3)
analytical geometry
1 Answer Available
Last Activity: 3 Years ago
A circle has its center on straight line 5x-2y+1=0 and cuts the x axis at two points whose absciasse are -5,3 find equation of the circle and it's radius.
A circle has its center on straight line 5x-2y+1=0 and cuts the x axis at two points whose absciasse are -5,3 find equation of the circle and it's radius.
analytical geometry
1 Answer Available
Last Activity: 4 Years ago
Prove that ax^2+by^2+cz^2 +2ux+2vy+2wz+d=0 represent a cone if u^2/a+v^/b+w^2/c=d
Prove that ax^2+by^2+cz^2 +2ux+2vy+2wz+d=0 represent a cone if u^2/a+v^/b+w^2/c=d
analytical geometry
1 Answer Available
Last Activity: 4 Years ago