Parabola Ellipse and Hyperbola

**varunnayudu** · December 23rd 2008, 01:25 AM

How will u classify the following curves in terms of parabola, ellipse or hyperbola?

i) $17x^2+12xy+8y^2-46x-28y+33=0$

ii) $x^2-5xy+y^2+8x-20y+15=0$

**mr fantastic** · December 23rd 2008, 04:10 AM

Originally Posted by varunnayudu

How will u classify the following curves in terms of parabola, ellipse or hyperbola?

i) $17x^2+12xy+8y^2-46x-28y+33=0$

ii) $x^2-5xy+y^2+8x-20y+15=0$

Read this: Conic section - Wikipedia, the free encyclopedia

**Soroban** · December 23rd 2008, 05:52 AM

Hello, varunnayudu!

How will u classify the following curves as parabola, ellipse or hyperbola?

$1)\;\;17x^2+12xy+8y^2-46x-28y+33\:=\:0$

$2)\;\;x^2-5xy+y^2+8x-20y+15\:=\:0$

If you are assigned "rotated" conics, you should have been given more information.

We know the curve is rotated due to the appearance of the $xy$ -term.

The general quadratic has the form: . $Ax^2 + Bxy + Cy^2 + Dx + Ey + F \;=\;0$

. . It has a "discriminant": . $\Delta \:=\:B^2-4AC$ . ... look familiar?

. . . . . . . . $\begin{array}{|c|c|}\hline \Delta \:=\:0 & \text{parabola} \\ \hline \Delta \:<\:0 & \text{ellipse} \\ \hline \Delta \:>\:0 & \text{hyperbola}\\ \hline \end{array}$

**zorro** · December 30th 2008, 08:55 PM

i have solved the two eq and got an answer but need to see if its right or wrong ...........Can u give what type of conic do the two eq form

**zorro** · January 11th 2009, 03:14 AM

Originally Posted by Soroban

Hello, varunnayudu!

If you are assigned "rotated" conics, you should have been given more information.

We know the curve is rotated due to the appearance of the $xy$ -term.

The general quadratic has the form: . $Ax^2 + Bxy + Cy^2 + Dx + Ey + F \;=\;0$

. . It has a "discriminant": . $\Delta \:=\:B^2-4AC$ . ... look familiar?

. . . . . . . . $\begin{array}{|c|c|}\hline \Delta \:=\:0 & \text{parabola} \\ \hline \Delta \:<\:0 & \text{ellipse} \\ \hline \Delta \:>\:0 & \text{hyperbola}\\ \hline \end{array}$

I have done it this way .Is this right.........

i) $17x^2 \ + \ 12xy \ + \ 8 y^2 \ - \ 46x \ - \ 28y \ + 33 \ = \ 0$

$a \ = \ 17 ; \ b \ = \ 8 ; h \ = \ 6;$

$ab-h^2 \ = \ 136 - 36 = \ 100$

since $ab-h^2 > 0$ therefore the eq is an hyperbola.

ii) $x^2 - 5xy + y^2 + 8x - 20y +15 = 0$

$a=1 ; \ b = 1; \ h = - \frac{5}{2}$

$\therefore \ ab-h^2 = 1 - \frac{25}{4} = \frac{4 - 25}{4} = - \frac{21}{4} \ = -5.25 \ < \ 0$

$\therefore since \ ab-h^2 < 0$ it is an ellipse.

Thread: Parabola Ellipse and Hyperbola

LinkBack

Thread Tools

Display

Parabola Ellipse and Hyperbola

can u give the answer

what do u think.

Similar Math Help Forum Discussions

need help with hyperbola and ellipse

hyperbola or parabola?

Parabola, Elipses, Hyperbola help?

Some Hyperbola, ellipse, parabola help.

Ellipse and Hyperbola

Search Tags