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LynFran
 one year ago
Show that (7,2) and (1,6) are on a circle whose center is (4,2) and find the length of the radius
LynFran
 one year ago
Show that (7,2) and (1,6) are on a circle whose center is (4,2) and find the length of the radius

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Do you know the standard equation for a circle?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[(xh)^2+(yk)^2 = r^2\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Where (h, k) are the center point

LynFran
 one year ago
Best ResponseYou've already chosen the best response.1ok with (h,k) being the center and r is the radius ..what nxt..

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Pick a point, (7,2): It can be odd sometimes, because the values may change sign

LynFran
 one year ago
Best ResponseYou've already chosen the best response.1ok so (3)^2+(4)^2=r^2 9+16=r^2 25=r^2 5=r ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So check if the points are in the circle

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Hmm, I think I did something wrong  (7,2) is in the circle, but not (1, 6)

LynFran
 one year ago
Best ResponseYou've already chosen the best response.1but we have to show that those points are on the circle

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sorry, I can't help you. It's been too long

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1ok... so the general form is \[(x  h)^2 + (y  k)^2 = r^2\] where (h, k) is the centre and r is the radius.. so if you substitute your centre you get \[(x  4)^2 + (y + 2)^2 = r^2\] is that ok so far...?

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1and reading the notes you have done the correct calculation so picking the point (7, 2) and substituting that you can find r^2 \[(7  4)^2 + (2 + 2)^2 = r^2\] so \[r^2 = 25\] so just take the square root of 25 to get the radius

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1it doesn't matter which point on the circle you use, as you'll get the same value so that just means the equation is \[(x  4)^2 + (y + 2)^2 = 25\]

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1hope it makes sense

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1f you want to check you can find the distance from the centre to the points using the distance formula and show the distance is 5 units

LynFran
 one year ago
Best ResponseYou've already chosen the best response.1but they say show that the points (7,2) and (1,6) are on the circle... i think thats what confuses me... idk how to show this...

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1sure so you know \[(7  4)^2 + (2 + 2)^2 = r^2\] using the other point \[(1  4)^2 + (6 + 2)^2 = r^2\] and you'll find \[r^2 = r^2 ~~~or~~~~25 = 25\]

LynFran
 one year ago
Best ResponseYou've already chosen the best response.1so \[\sqrt{(71)^2+(2+6)^2}=10\]

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1so since both points are the same distance from the centre, by definition, the points are on a circle centre (4, 2) and radius 5

LynFran
 one year ago
Best ResponseYou've already chosen the best response.1oh \[\sqrt{(41)^2+(2+6)^2}=5\]

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1I wouldn't find the distance between the points. I'd use distance from the centre to each point... which is really the same as substituting into the general form to show that the radius is equal. A simple definition of a circle is a set of points equidistant from a fixed point. so showing that the radius is 5 from both points to a fixed point( the centre) then the 2 points are on a circle, centre (4, 2) and radius 5

LynFran
 one year ago
Best ResponseYou've already chosen the best response.1and \[\sqrt{(47)^2+(22)^2}=5\]

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1that works.... so you have shown the points are the same distance from the fixed point
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