Find the equation of the circle in general forn if the diameter is 12 and the center is 8,1? Thabk you for the answer

2 Answers
Alan P.
Jun 20, 2018

#(x-8)^2+(y-1)^2=6^2#

Explanation:

If the diameter is #12# then the radius is #12/2=6#

The general equation of a circle with center #(a,b)# and radius #r# is
#color(white)("XXX")(x-a)^2+(y-b)^2=r^2#

Tony B
Jun 25, 2018

#(x-8)^2+(y-1)^2=6^2#

Explanation:

The equation of a circle is basically using Pythagoras #a^2+b^2=c^2#

It is just that we are using the x-axis value as say #a#, the y-axis value as say #b# and the radius of the circle as #c#

If the centre is at the origin we have #x^2+y^2=r^2#

This works very well when centred at at the origin but what if it is elsewhere?

We 'hypothetically' take it back to the origin

So if the centre is at 8 on the x-axis we write #(x-8)#
So if the centre is at 1 on the y-axis we write #(y-1)#

The length of the radius is unchanged giving:

#(x-8)^2+(y-1)^2=r^2=(12/2)^2#

Related questions
Impact of this question
2746 views around the world
You can reuse this answer
Creative Commons License