(i) Let
S be the focus and
be any point on the hyperbola.
Draw PM perpendicular to the directrix.
![](https://search-static.byjusweb.com/question-images/meritnation_ana/img/study_content/content_ck_images/images/2_119.png)
By definition:
SP = ePM
Squaring both the sides:
∴ Equation of the hyperbola =
(ii) Let
S be the focus and
be any point on the hyperbola.
Draw PM perpendicular to the directrix.
By definition:
SP = ePM
![](https://search-static.byjusweb.com/question-images/meritnation_ana/img/study_content/content_ck_images/images/2_214.png)
Squaring both the sides:
∴ Equation of the hyperbola =
(iii) Let
S be the focus and
be any point on the hyperbola.
Draw PM perpendicular to the directrix.
By definition:
SP = ePM
![](https://search-static.byjusweb.com/question-images/meritnation_ana/img/study_content/content_ck_images/images/2_310.png)
Squaring both the sides:
∴ Equation of the hyperbola =
(iv) Let
S be the focus and
be any point on the hyperbola.
Draw PM perpendicular to the directrix.
![](https://search-static.byjusweb.com/question-images/meritnation_ana/img/study_content/content_ck_images/images/2_47.png)
By definition:
SP = ePM
= ePM
Squaring both the sides:
∴ Equation of the hyperbola =
(v) Let
S be the focus and
be any point on the hyperbola.
Draw PM perpendicular to the directrix.
![](https://search-static.byjusweb.com/question-images/meritnation_ana/img/study_content/content_ck_images/images/2_56.png)
By definition:
SP = ePM
Squaring both the sides:
∴ Equation of the hyperbola =
(vi) Let
S be the focus and
be any point on the hyperbola.
Draw PM perpendicular to the directrix.
By definition:
SP = ePM
![](https://search-static.byjusweb.com/question-images/meritnation_ana/img/study_content/content_ck_images/images/2_6.png)
Squaring both the sides:
∴ Equation of the hyperbola =