Question

If focus and corresponding directrix of an ellipse are (3,4) and x+y-1=0 respectively and eccentricity is 1/2 then find the coordinates of extremities of major

Answer 1

Answer: The length of major axis is 2*2^(1/2).

Step-by-step explanation:

Suppose, we have given a point and an equation of line

ax+by+c=0

(h,k)

The formula of perpendicular distance between the line and the point is:

d= mod(ah+bk+c)/(a^2+b^2)^(1/2)

In this question,

The perpendicular distance between the directrix and the corresponding focus would be

d= mod(3+4-1)/(1^2+1^2)^(1/2)

d= 6/2^(1/2)=3*2^(1/2)

We know

e= length of focus/major axis= f/a

So, f= ae

and e= major axis/distance from the center to the directrix= a/D

So, D= a/e

Thus, d= D-f

=> 3*2^(1/2)= a/e-ae

=> 3*2^(1/2)= 2a-a/2

=> 3*2^(1/2)= 3/2a

=> a= 2*^(1/2)