Question

What conic section is this?

Answer 1

And how do I graph it.

7y^2 - 5x + 20x = 3

It doesn't look like a circle, parabola, hyperbola or an ellipse to me...

Answer 2

circle - has an x^2 and y^2 with the same coeff.

parabola - has only x^2 OR y^2

ellipse - x^2 and y^2, different coefficients, but both the same sign

hyperbola - x^2 and a y^2 but different signs

Memorize that.

Answer 3

So it is a hyperbola then. Sorry, the 5x is supposed to be squared.

What threw me off was the 20x... I've never dealt with two x variables in the same equation before (not while graphing conics, anyway). So I'm not quite sure what to do.

Answer 4

By coefficient, do you mean the denominator?

Answer 5

Coefficient of x^2 means the number in front of x^2

Answer 6

But \[x^2/25 + y^2/9 = 1 \] is an ellipse, and the coefficients are the same, right?

Answer 7

You still there? :/ I've been on this problem for an hour and a half.

Answer 8

\[\Large \frac{ x^2 }{ 25 }= \frac{ 1 }{ 25 }x^2\]

Answer 9

\[\large \frac{ 1 }{25 } x^2 +\frac{ 1 }{ 9 } y^2 = 1\]

Answer 10

How did you get that?

Answer 11

Can someone actually help me with this problem?

Answer 12

First of all, did you mean for there to be an x^2 ?

Answer 13

Yes, here is the equation: 7y^2 - 5x^2 + 20x = 3

Thank you so much!

Answer 14

By the way an ellipse is like an oval/football shape. So if there coefficients are the same (like in that hypothetical example you gave earlier) it is indeed an ellipse, but more correctly a circle. A circle is pretty much an ellipse, like you could call a square a rectangle.

Answer 15

Okay so you have 2 squared variables. Which cancels out the option of a parabola, correct?

Answer 16

@Abbles i showed you how to identify it:
you gave \[\large x^2/25 + y^2/9 = 1 \]which is the same as \[\large \frac{ 1 }{25 } x^2 +\frac{ 1 }{ 9 } y^2 = 1 \]Look at the coefficients.

Answer 17

Right. I was thinking it was a hyperbola because the signs are different, but I don't know

Answer 18

You already knew the first equation was a hyperbola, when you said "So it is a hyperbola then. "

Answer 19

Yeah but you never confirmed or denied it so I wasn't sure. It was a guess

Answer 20

It is a hyperbola, but you can change how the equation looks so it looks more familiar to you. Would you like me to show you how to do that?

Answer 21

Yes please!

Answer 22

Are you familiar with "completing the square"?

Answer 23

@Abbles i gave you a medal. If you were wrong, i would've said so.

Answer 24

Yes I am familiar with it. And why couldn't you have just said yes? lol

Answer 25

Because you didn't appear to be guessing. You seemed confident, i gave you a medal for being correct.

Answer 26

BTW you absolutely don't need to complete the square to identify these. All you need is:

circle - has an x^2 and y^2 with the same coeff.

parabola - has only x^2 OR y^2, not both

ellipse - has an x^2 and y^2, different coefficients, but both the same sign

hyperbola - has an x^2 and a y^2 but different signs

Answer 27

I need to know how to get it into standard form.

Answer 28

Make a new question for standard form, this is long enough already

Answer 29

Yeah you can do what @agent0smith said to identify it, but putting it into standard form can help you visualize it better.

Answer 30

\[7y^2-5(x^2-4x+4-4)=3\]
\[7y^2-5(x-2)^2+20=3,7y^2-5(x-2)^2=-17\]
divide by -17
\[\frac{ 7y^2 }{ -17 }-\frac{ 5(x-2)^2 }{ -17 }=1\]
\[\frac{ \left( x-2 \right)^2 }{ \frac{ 17 }{ 5 } }-\frac{ y^2 }{ \frac{ 17 }{ 7 } }=1\]
which is a hyperbola,where
\[a^2=\frac{ 17 }{ 5 },b^2=\frac{ 17 }{ 7 }\]

Answer 31

Where did you get the (x2−4x+4−4) from? Thanks for the help!

Answer 32

to complete the square add {(co-efficient of x)/2}^2
4/2=2
and square of 2=4
we add 4 and subtract 4 so that equation remains same.

Answer 33

Oh okay. So that would be the equation in standard form?

Answer 34

The center would be at (2, 0) right?

Answer 35

And it is a horizontal hyperbola?

Answer 36

Yes; yes.

Answer 37

Thank you guys so much! Whew :) Been a long day of math.

Answer 38

Welcome, but keep in mind you are expected to identify these just from the equation, not in standard form.

Answer 39

You should be able to identify these with what i gave earlier, you only need to look at the x^2 and y^2 terms, nothing else matters
\[\large 5x^2 + 10y^2 +11y-17x +5 = 0\]
\[\large 5x^2 +11y-17x +5 = 0\]
\[\large 5x^2 - 10y^2 +11y-17x +5 = 0\]
\[\large 5x^2 + 5y^2 +11y-17x +5 = 0\]

Answer 40

I'll study up!

Answer 41

You should be able to identify them, right now :P

circle - has an x^2 and y^2 with the same coeff.

parabola - has only x^2 OR y^2, not both

ellipse - has an x^2 and y^2, different coefficients, but both the same sign

hyperbola - has an x^2 and a y^2 but different signs

Answer 42

The first one is an ellipse, the second one is a parabola, the third is a hyperbola and the fourth is a circle. Amirite?:)

Answer 43

Right :)