IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry

flowers_rsss

1))If one of the focus of the hyperbola is (3,0) and its corresponding directrix is x+y=0.if its eccentricity is 2,the length of the intercept on x-axis is??

2))how to find ecentricity of an ellipse of the form ax^2+2hxy+by^2+2gx+2fy+c=0.

plss help!!!!!!!!

flowers_rsss

pls anyone!!!

dinesh_ddt

how can a hyperbola have a intercept(in this case)?????????

a5hw1n_5

for the 1st one
u know tht
PS/PM=e where PS is the dist of any pt P(x,y) on the hyp frm the focus and PM is the dist frm the directrix.
using this,
we get
PS=

((x-3)² +y²)
PM= (x+y)/

2

PS/PM=

(2 (x-3)² +y²)/(x+y)= 2

since the intercepts lie on the x axis let the pts be (x1,0), (x2,0) which we get by
sub y=0 and solving the eq

(2 (x-3)²)/(x)= 2
so we get
x1= -3

2/(2-

2)
x2= 3

2/(2+

2)
hence the length is
6

2 units

i didnt get the 2nd one

flowers_rsss

your answer for the first is exactly correct.

flowers_rsss

can anyone try the second one
pls!!!!

Ask & Discuss Questions with Community & Experts