Are the identities correct for the following conic sections?

• Aug 21st 2009, 04:44 AM
bobbyboy1111
Are the identities correct for the following conic sections?
Are the identities correct for the following conic sections? Also, is the work for each equation correct? Each is supposed to be solved for y. Thanks will be give to those who help(Clapping)

1. 25x^2 - 9y^2 = 144

-9y^2 = -25x^2 + 144

-9y^2/-9 = -25x^2/-9 + 144

y^2 = -25x^2/-9 + 144

y = +_SQRT(-25x^2/-9 + 144)

Hyperbola

2. x^2 + y^2 = 225

y^2 = -x^2 + 225
y = +_SQRT(-x^2 + 225)

Ellipse

3. x^2 + 3y^2 = 3

3y^2 = -x^2 + 3

3y^2/3 = -x^2/3 + 3

y^2 = -x^2/3 + 3

y = +_SQRT(-x^2/3 + 3)

Ellipse

• Aug 21st 2009, 09:22 AM
Hello bobbyboy1111
Quote:

Originally Posted by bobbyboy1111
Are the identities correct for the following conic sections? Also, is the work for each equation correct? Each is supposed to be solved for y. Thanks will be give to those who help(Clapping)

1. 25x^2 - 9y^2 = 144

-9y^2 = -25x^2 + 144

-9y^2/-9 = -25x^2/-9 + 144

y^2 = -25x^2/-9 + 144

y = +_SQRT(-25x^2/-9 + 144)

Hyperbola

2. x^2 + y^2 = 225

y^2 = -x^2 + 225
y = +_SQRT(-x^2 + 225)

Ellipse

3. x^2 + 3y^2 = 3

3y^2 = -x^2 + 3

3y^2/3 = -x^2/3 + 3

y^2 = -x^2/3 + 3

y = +_SQRT(-x^2/3 + 3)

Ellipse

(1) Yes, it's a hyperbola; no, your working is incorrect. When you divided by -9, you forgot to divide the 144.

$\displaystyle y = \pm\sqrt{\frac{-25x^2+144}{-9}} =$
$\displaystyle \pm\sqrt{\frac{25x^2-144}{9}} = \pm\frac{\sqrt{25x^2-144}}{3}$

(2) Yes, it is an ellipse, but more than that, it's actually a circle. Your working is correct.

(3) Yes, it is an ellipse, but you forgot to divide the constant term again.

$\displaystyle y = \pm\sqrt{\frac{3-x^2}{3}}$