Centre and radius of (x+4)^2+(y-1)^2=13?

Centre (-4,1), radius \sqrt{13}.

How do you find the radius from the centre and a point on the circle?

Find the distance between them; r^2 is the sum of the squared differences.

How do you find the centre if you know the ends of a diameter?

Find the midpoint of the diameter.

How do you find the centre of x^2+y^2-10x+4y+13=0?

Complete the square: (x-5)^2+(y+2)^2=16, centre (5,-2).

How do you decide whether a point is inside the circle?

Compare (p-a)^2+(q-b)^2 with r^2: less than means inside.

How do you find where a circle meets the x-axis?

Put y=0 into the equation and solve.

Equation of a circleEdexcel International A Level Maths: Flashcards

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What is the equation of a circle with centre $(a,b)$ and radius $r$?

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What is the equation of a circle with centre $(a,b)$ and radius $r$ ?: $(x-a)^2+(y-b)^2=r^2$
What is the equation of a circle with centre the origin and radius $r$ ?: $x^2+y^2=r^2$
Centre and radius of $(x-3)^2+(y+2)^2=25$ ?: Centre $(3,-2)$ , radius $5$ .
Centre and radius of $(x+4)^2+(y-1)^2=13$ ?: Centre $(-4,1)$ , radius $\sqrt{13}$ .
What is on the right-hand side of the circle equation?: $r^2$ , the radius squared.
How do you find the radius from the centre and a point on the circle?: Find the distance between them; $r^2$ is the sum of the squared differences.
How do you find the centre if you know the ends of a diameter?: Find the midpoint of the diameter.
Midpoint of $(-3,1)$ and $(5,5)$ ?: $(1,3)$
How do you find the centre of $x^2+y^2-10x+4y+13=0$ ?: Complete the square: $(x-5)^2+(y+2)^2=16$ , centre $(5,-2)$ .
How do you decide whether a point is inside the circle?: Compare $(p-a)^2+(q-b)^2$ with $r^2$ : less than means inside.
How do you find where a circle meets the $x$ -axis?: Put $y=0$ into the equation and solve.
Greatest $y$ on a circle with centre $(a,b)$ and radius $r$ ?: $b+r$

Exam questions on Equation of a circle

A circle has equation $(x-3)^2+(y+2)^2=25$ .
Determine whether the point $(6,2)$ lies inside, outside or on the circle.2 marks
A circle has centre $(-4,1)$ and passes through the point $(-2,4)$ .
Find the coordinates of the points where the circle meets the line $y=1$ .2 marks
A circle $C$ has equation $x^2+y^2-10x+4y+13=0$ .
Find the coordinates of the centre of $C$ and the radius of $C$ .3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).