What Are the Key Steps to Solve These Ellipse Problems?

[trigger352]

Problem I:

(The coeffiecients throw me off, I don't know what I'm supposed to do with them)
9x^2 + 16y^2 = 144

Determine:
a) coodinates of the centre
b) lengths of the major and minor axes




Problem II:

Sketch a graph of the ellipse

4x^2 + (y+1)^2 = 9




PS: For future posts would it be of any help to include the textbook referred to etc?

In this case:

Mathpower 12: WE
Problem I - p. 150 #9
Problem II - p. 150 #19

PPS: I've also italicized any comments about my attemts - since people seem to like to help out people making an attempt.

 

[sportsguy3675]

Problem I:

(The coeffiecients throw me off, I don't know what I'm supposed to do with them)
9x^2 + 16y^2 = 144

Determine:
a) coodinates of the centre
b) lengths of the major and minor axes

You have to get it in standard form first. Divide both sides by 144.

That gives:

$$\frac{x^2}{16} + \frac{y^2}{9} = 1$$

a = length of the major axis
b= length of the minor axis

 

[ViktigLemma]

The clue in both the exercises is to recognize the form of an ellipse with its centre in the origin:

$$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$

As mentioned a and b are the lengths of the axes.


In the second exercise the centre is not in origo but (x=0,y=-1).