(a) A hyperbola in standard position has equation 36x2 - 49y? - 100 = 0. (i) Find the vertices and asymptotes of the hyperbola. (ii) Sketch the hyperbola, labelling its vertices with their coordinates and its asymptotes with their equations. (iii) Find the eccentricity, foci and directrices of the hyperbola.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 35E
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(a) A hyperbola in standard position has equation
36x2 – 49y? - 100 = 0.
(i) Find the vertices and asymptotes of the hyperbola.
(ii) Sketch the hyperbola, labelling its vertices with their coordinates
and its asymptotes with their equations.
(iii) Find the eccentricity, foci and directrices of the hyperbola.
(iv) Write down a parametrisation of the part of this hyperbola that
lies in the second quadrant (not including any points that lie on
the x-axis or y-axis). Make sure that you include the restrictions
that are needed on the values of the parameters.
Transcribed Image Text:(a) A hyperbola in standard position has equation 36x2 – 49y? - 100 = 0. (i) Find the vertices and asymptotes of the hyperbola. (ii) Sketch the hyperbola, labelling its vertices with their coordinates and its asymptotes with their equations. (iii) Find the eccentricity, foci and directrices of the hyperbola. (iv) Write down a parametrisation of the part of this hyperbola that lies in the second quadrant (not including any points that lie on the x-axis or y-axis). Make sure that you include the restrictions that are needed on the values of the parameters.
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