VCE Specialist 3/4 Question Thread!

[Talia2144]

HI, can anyone please help with question: the equation: x^2+ax+y^2=0, where a is a real constant; will represent a circle if A(a<-2 only)
B(a>-2 only)
C(a=+-2 only)
D(-2<a<2)
E(a<-2 or a>2)
Thank you

[keltingmeith]

HI, can anyone please help with question: the equation: x^2+ax+y^2=0, where a is a real constant; will represent a circle if A(a<-2 only)
B(a>-2 only)
C(a=+-2 only)
D(-2<a<2)
E(a<-2 or a>2)
Thank you

Remember, the general equation of a circle is . So, let's put our equation into that form:



Now, we need to complete the square of that circle - this means that we require , which gives us:



Now, from this, we can see that we have a circle as long as . This doesn't work with any of those answers - so, I'm going to assume that the question means a circle with radius one. This means we require , which is C.

[Talia2144]

thank you i took a look at the working out, however my teacher has given the answer as E

[keltingmeith]

thank you i took a look at the working out, however my teacher has given the answer as E

Which corresponds to a circle with a radius greater than 1, which may have been what your teacher wanted to ask/thought was being asked.

As I said, that equation will represent a circle so long as a=/=0, so we need more information to pick an option.

[cosine]

ok thank you for the help, I appreciate it 

Guys, I am assuming you are just starting the subject, how come you are doing this stuff? Is every school's course different, because my school is starting with vectors, and does it matter which topic you start from?

[Talia2144]

our schooling starting with coordination geometry, this topic this repetitive question. overall it does not matter which topic you start but it does matter with some topic as an introduction has to be done in methods in order to proceed with specialist 

[Talia2144]

sorry for repeating this question but i want to know how to proceed with the question if i add 1
 HI, can anyone please help with question: the equation: x^2+ax+y^2=0 becomes x^2+ax+y^2+1=0, where a is a real constant; will represent a circle if
A(a<-2 only)
B(a>-2 only)
C(a=+-2 only)
D(-2<a<2)
E(a<-2 or a>2)
Thank you

[lArcdeTriomphe]

In this case, after rearranging, you would get:

(basically the same as what eulerfan posted, but with a '-1' at the end).

a circle would only exist if its radius is greater than 0.
since r>0, it follows that 

since , therefore
     
 
-->
doing a quick sketch of a parabola would give you as the possible values of a for which there is a circle
i.e. E

[keltingmeith]

Guys, I am assuming you are just starting the subject, how come you are doing this stuff? Is every school's course different, because my school is starting with vectors, and does it matter which topic you start from?

As long as you've covered everything in the study design by the end of the year, you're fine. Each teacher thinks there is a better way of tackling the course than another, and there's nothing wrong with each individual way, they just have different advantages.

an introduction has to be done in methods in order to proceed with specialist

Not technically true - sure, the idea is that you learn calculus and algebra in methods so that you can use it in specialist, however it's often the case that methods just moves too slowly for specialist to teach it efficiently. When I did specialist last year, our spec teacher taught us the basics of differentiation and integration that we needed, because we didn't have the time to wait for the methods classes to catch up.

[cosine]

As long as you've covered everything in the study design by the end of the year, you're fine. Each teacher thinks there is a better way of tackling the course than another, and there's nothing wrong with each individual way, they just have different advantages.

Thanks for that, EulerFan!
By the way, does that program where you can write math symbols work for macs?
I downloaded it but it wont load lol

[Zues]

part c and part d, also if you could draw a graph to help explanation. (i assume its a trigonemetric graph??)

[keltingmeith]

Thanks for that, EulerFan!
By the way, does that program where you can write math symbols work for macs?
I downloaded it but it wont load lol

Hahah, you mean MiKTeX? Pretty sure it does if you get the right version, but you don't need the program to use it on the forums (however might find it useful if you ever engage in mathematics/science education in university). Just use the tex tags - ie, if you write (tex)stuff(/tex) (using square brackets instead of round), the "stuff" part will be in "maths symbol mode". Feel free to pick a random topic, write a new post, and play around using "preview" instead of actually posting.

[keltingmeith]

part c and part d, also if you could draw a graph to help explanation. (i assume its a trigonemetric graph??)

c and d require the identity . If you have not yet covered the reciprocal circular functions, just ignore these until you have covered them.

[Zues]

why have they said a is square root 3 on 2, as apposed to square root 2

[Zues]

can someone also please work it out