Is a circle equation a quadratic equation?

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marcus888
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Hi there .

I have been studying 'solving linear and quadratic simultaneous equations' and there are a few questions that include equations of a circle in the same section of my text book (I have attached one).

Does that mean a circle equation is a quadratic? If so, how is it as I thought as quadratic needed to be of the form ax^2 + bx + c

Could someone explain please?

Thanks
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thefatone
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(Original post by marcus888)
Hi there .

I have been studying 'solving linear and quadratic simultaneous equations' and there are a few questions that include equations of a circle in the same section of my text book (I have attached one).

Does that mean a circle equation is a quadratic? If so, how is it as I thought as quadratic needed to be of the form ax^2 + bx + c

Could someone explain please?

Thanks
no the equation of a circle is in the form

\left(x+a\right)^2 +\left(y+b\right)^2 = r^2

to get the equation of the circle you need the centre of the circle and the diameter or something to work out the radius

so in your example the centre of that circle is 0,0
so so we know that in the equation i posted above that where a and b are 0 we are left with x²+y²=r²

we know the diameter is 4 so half it to get the radius which is 2 and square it to get the r² which is 4

so we have x²+y²=4


for part b just use substitution to get a value for x or y then sub in to one of the original equations to get the other co-ordinate
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Lemuelc14
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(Original post by marcus888)
Hi there .

I have been studying 'solving linear and quadratic simultaneous equations' and there are a few questions that include equations of a circle in the same section of my text book (I have attached one).

Does that mean a circle equation is a quadratic? If so, how is it as I thought as quadratic needed to be of the form ax^2 + bx + c

Could someone explain please?

Thanks
is it solving the equation you need help with?
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Sir Cumference
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(Original post by marcus888)
Hi there .

I have been studying 'solving linear and quadratic simultaneous equations' and there are a few questions that include equations of a circle in the same section of my text book (I have attached one).

Does that mean a circle equation is a quadratic? If so, how is it as I thought as quadratic needed to be of the form ax^2 + bx + c

Could someone explain please?

Thanks
No a circle equation is not a quadratic.

From the Edexcel specification:

"Solve exactly, by elimination of an unknown, two simultaneous equations in two unknowns, one of which is linear in each unknown, and the other is linear in one unknown and quadratic in the other, or where the second equation is of the form x^2+y^2=r^2."
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marcus888
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(Original post by Lemuelc14)
is it solving the equation you need help with?
No, I can solve it fine. I am just asking if the equation of a circle is a quadratic equation as there are a few of these types under the section saying 'solving quadratic and linear simultaneous equations'.
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EricPiphany
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(Original post by marcus888)
Hi there .

I have been studying 'solving linear and quadratic simultaneous equations' and there are a few questions that include equations of a circle in the same section of my text book (I have attached one).

Does that mean a circle equation is a quadratic? If so, how is it as I thought as quadratic needed to be of the form ax^2 + bx + c

Could someone explain please?

Thanks
It is technically a quadratic, see Wikipedia's entry for 'Quadratic function'.
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Pangol
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Since "quadratic" means "highest power of the variable is 2", then the equation of a circle is a quadratic equation. The unusal thing, compared to the quadratic equations that are normally met at A level, is that it is a quadratic equation in two variables, x and y. In all of the A level specifications, a quadratic equation is taken to mean a quadratic equation in only one variable.

So; when a specification says "quadratic equation", they mean one in one variable only. This would not include circles. They would specifically talk about circles if that is what they mean. Technically, circles are quadratics, but since they are quadratic in two variables, this is not what the specifications mean by quadratic.
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Zacken
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(Original post by EricPiphany)
It is technically a quadratic, see Wikipedia's entry for 'Quadratic function'.
(Original post by Pangol)
Since "quadratic" means "highest power of the variable is 2", then the equation of a circle is a quadratic equation. The unusal thing, compared to the quadratic equations that are normally met at A level, is that it is a quadratic equation in two variables, x and y. In all of the A level specifications, a quadratic equation is taken to mean a quadratic equation in only one variable.

So; when a specification says "quadratic equation", they mean one in one variable only. This would not include circles. They would specifically talk about circles if that is what they mean. Technically, circles are quadratics, but since they are quadratic in two variables, this is not what the specifications mean by quadratic.
There's (apparently) a difference between a quadratic equation (1) (2) and a quadratic/quadratic function. (1)
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EricPiphany
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(Original post by Zacken)
There's (apparently) a difference between a quadratic equation (1) (2) and a quadratic/quadratic function. (1)
Maybe. And perhaps we can say that the term 'simultaneous quadratic' implies in more than one variable.
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atsruser
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(Original post by Zacken)
There's (apparently) a difference between a quadratic equation (1) (2) and a quadratic/quadratic function. (1)
Apparently? Of course they're different - there's a difference between a function (f : A \to B) and an equation (f(x)=f(y)) - they're totally different things.
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Zacken
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(Original post by atsruser)
Apparently? Of course they're different - there's a difference between a function (f : A \to B) and an equation (f(x)=f(y)) - they're totally different things.
Well, yes. Bad wording on my part. I was referencing the fact that one was univariate and the other wasn't.
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atsruser
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(Original post by Zacken)
Well, yes. Bad wording on my part. I was referencing the fact that one was univariate and the other wasn't.
OK I see. However, I'm not sure that I agree with that definition of a quadratic equation; for me, any equation in n variables with highest power two is quadratic - if not, then what is it called?
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Gregorius
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The terminology in this areas is somewhat fluid and ambiguous; but just to throw another one into the ring, let me introduce the notion of a quadric.
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DavidBy
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The result of a st. line intersecting with a circle is a quadratic, as the cross at 2 points. the solution of the resulting quadratic are the x values of the 2 points
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