(a)
Given
It can be written as
Comparing it with general conic section
, we get
, since e i.e. eccentricity lies between 0 & 1. :. given conic section is ellipse.
for x-intercept
,
so x-intercept in this case is (1/2, 0)
when
, so x-intercept in this case is
for y-intercept
when
, so y-intercept in this case is
when
, so y-intercept in this case is
One foci is (0, 0) of this form. Now, to find other foci we will find out center of the ellipse & it will be the mid point of both the x-intercepts
i.e. center
Now we will distance of center
and 1st foci
since the distance of both the foci from the center is same, so coordinates of 2nd foci is
i.e.
so, x intercepts are
y intercepts are
foci are
(b)
Given
It can be written as
Comparing it with general conic section
, we get
, since e i.e. eccentricity is greater than
given conic section is hyperbola.
for x-intercept
when
, so x -intercept in this case is
when
,so x -intercept in this case is
for y-intercept
when
, so y-intercept in this case is
when
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