SOLUTION: please help me identify the following conic. That is, is it a circle, parabola, hyperbola or ellipse? show why please!!! x^2 - 4y^2 - 4x - 24y = 48

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: please help me identify the following conic. That is, is it a circle, parabola, hyperbola or ellipse? show why please!!! x^2 - 4y^2 - 4x - 24y = 48      Log On


   

Question 93595This question is from textbook
: please help me identify the following conic. That is, is it a circle, parabola, hyperbola or ellipse? show why please!!! x^2 - 4y^2 - 4x - 24y = 48 This question is from textbook

Found 2 solutions by stanbon, psbhowmick:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 - 4y^2 - 4x - 24y = 48
----------
It's a hyperbola because the signs of the coefficients of x^2 and
of y^2 are different.
-------------
Cheers,
Stan H.

Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
Given equation: x%5E2+-+4y%5E2+-+4x+-+24y+-+48+=+0

Compare with the standard equation for a conic
ax%5E2+%2B+2hxy+%2B+by%5E2+%2B+2gx+%2B+2fy+%2B+c+=+0
If h%5E2+-+ab+=+0 then the conic is a parabola.
If h%5E2+-+ab+%3C+0 then the conic is an ellipse.
If h%5E2+-+ab+%3E+0 then the conic is a hyperbola.
If a+=+b and h+=+0 then the conic is a circle.

Here, a = 1, b = -4, h = 0.
So h%5E2+-+ab+=+4+%3E+0 and hence the conic is a hyperbola.