+0

# Identify the conic section? Is my answer correct?

0
388
5
+41

Identify the conic section.

4x^2 + 7y^2 + 32x - 56y + 148 = 0

Correct me if I'm wrong, but I think it's  hyperbola with center (4, 4) and foci at (-4, 5.73), (-4, 2.27)?

thanks!

tylersomers2000  Mar 27, 2015

#4
+91962
+10

NOTE that your earlier hyperbola had a minus sign between the squared terms

and

The ellipse as a positive sign.   If the numbers on  the botton were the same then it would be a circle.

A circle is a special case of an elipse because it has a double focii instead of 2 separate focii.

Effectively a cirlce has one centre and other ellipses have 2 centres.

Melody  Mar 27, 2015
Sort:

#1
+91962
+10
Melody  Mar 27, 2015
#5
+776
0

OMG!!! you use desmos to!!!!!!!

User101  Apr 16, 2016
#2
+91962
+10

$$\\4x^2 + 7y^2 + 32x - 56y + 148 = 0 \\\\ 4x^2+ 32x + 7y^2 - 56y =-148 \\\\ 4(x^2+8x)+7(y^2-8y)=-148\\\\ 4(x^2+8x+16)+7(y^2-8y+16)=-148+4*16+7*16\\\\ 4(x+4)^2+7(y-4)^2=28\\\\ \frac{4(x+4)^2}{28}+\frac{7(y-4)^2}{28}=1\\\\ \frac{(x+4)^2}{7}+\frac{(y-4)^2}{4}=1\\\\ \frac{(x+4)^2}{(\sqrt7)^2}+\frac{(y-4)^2}{2^2}=1\\\\$$

This is an ellipse centre (-4,+4)

The ends of the major axis are   $$(-4-\sqrt7,4) and (-4+\sqrt7,4)$$

Then ends of the minor axis are  (-4,4-2) (-4,4+2)  that is    $$(-4,2) and (-4,6)$$

references

http://www.mathsisfun.com/geometry/ellipse.html

http://en.wikipedia.org/wiki/Ellipse

Melody  Mar 27, 2015
#3
+91962
+3

Oh and Welcome to the forum Tyler :)

Melody  Mar 27, 2015
#4
+91962
+10

NOTE that your earlier hyperbola had a minus sign between the squared terms

and

The ellipse as a positive sign.   If the numbers on  the botton were the same then it would be a circle.

A circle is a special case of an elipse because it has a double focii instead of 2 separate focii.

Effectively a cirlce has one centre and other ellipses have 2 centres.

Melody  Mar 27, 2015

### 12 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details