Welcome :: Homework Help and Answers :: Mathskey.com
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,434 questions

17,804 answers

1,438 comments

47,372 users

Write the equation in standard form for the hyperbola with vertices (4,0) & (-4,0) and asymptote y=(1/4)x &?

0 votes
Write the equation in standard form for the hyperbola with vertices (4,0) & (-4,0) and asymptote y=(1/4)x & y=-(1/4)x.

Please help me and explain. Thank you.
asked Feb 5, 2013 in PRECALCULUS by homeworkhelp Mentor

2 Answers

+2 votes

The graph of the equation on the left has the following properties: x intercepts at ± a , no y intercepts, foci at (-c , 0) and (c , 0), asymptotes with equations y = ± x (b/a)

The hyperbola standard form is x2/a2 + y2/b2 = 1------>(1)

Given that vertices (4,0) & (-4,0) and asymptote y=(1/4)x & y=-(1/4)x.

asymptotes with equations y = ± x (b/a) = ± x (1/4)

So, a = 4 and b = 1.

Substitute a = 4 and b = 1 in the equation(1).

[( x2/42) + (y2/12)] =1

[( x2/16) + (y2/1)] =1

The hyperbola standard form is x2/16 + y2/1 = 1

answered Feb 5, 2013 by richardson Scholar
0 votes

The vertices of hyperbola is (4, 0) and (- 4, 0) and asymptote y = ± (1/4)x.

The standard form of equation of hyperbola with center at the origin (where a and b are not equals to 0) is x 2/a 2 - y 2/b 2 = 1 (Transverse axis is horizontal) or y 2/a 2- x 2/b 2 = 1 (Transverse axis is vertical).

The x - coordinates of the  vertices points are 4 and - 4.

The value of a = 4, because the vertices are four units from the center.

Because the transverse axis is horizontal, the asymptotes are of the forms y = (b/a) x and y = - (b/a) x.

The asymptote y = ± (1/4)x is comparison with y = ± (b/a) x.

b/a = 1/4 ------> b = 1 and a = 4.

The standard form of the hyperbola equation is x 2/4 2 - y 2/1 2 = 1.

answered Jun 30, 2014 by lilly Expert
edited Jun 30, 2014 by lilly

Related questions

...