The vertices of a hyperbola are and

MATHEMATICS · Multi-part · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

The vertices of a hyperbola are

V_{1}(-6,0)

and

V_{2}(6,0)

, and its asymptotes are the straight lines

y=\frac{2}{3}x

and

y=-\frac{2}{3}x

. (i) Find the values of

a

and

b

for the hyperbola. (ii) Write its standard equation in simplest form. (iii) Calculate the coordinates of its foci. (iv) Sketch the hyperbola on suitable axes, showing and labelling the centre, vertices, foci, and asymptotes.

Related theory

Hyperbola
Conic Sections
Coordinate Geometry
Hyperbola standard equation

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