SOLUTION: Hey :D i attemped this geometry based homework 2 weeks ago, i managed to do questions 1,2,3,4,5,6, which i found challenging as circles arent my strong point :D i tried for

Question 122053This question is from textbook AS core for edexcel, advanced maths.
: Hey :D
i attemped this geometry based homework 2 weeks ago, i managed to do questions 1,2,3,4,5,6,
which i found challenging as circles arent my strong point :D i tried for twice to do questions 7,8,9.
With no luck, it has driven me actually crazy, ive tried so hard, and when i got it back earlier today he said, try again.
So i would really appreciate if someone could help me on these 3 questions, i have a headache from them now, i just wanna know how to do them :(

7.
Find the equation of the circle whose centre is (3, -5) and which passes through the point (6, -7).
( i thought i was really getting somewhere with this question, i think just a small thing i must have done wrong somewhere).
8.
The points (10, -4) and (2,2) are the ends of a diameter of a circle, find the equation of the circle?
I went along the lines of finding the radius by halving... etc, again, something i think only small occured wrong.
9. ( this i cant do at all)
they give 3 points on a circle and must find the equation from only 3 points in a circle.
I have NO idea in the world how to do this, please help :D

a circle passes through the points (6,3), (-5,2) and (7,2) , find the equation of the circle.

Thank you SO much for anyhelp, im sorry for asking so much, but ive tried 2 days, tried really hard to understand it, read textbooks and internet pages :( Im sorry but i really need help thanks you SO much! This question is from textbook AS core for edexcel, advanced maths.

Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
the general equation for a circle is (x-h)^2+(y-k)^2=r^2 __ (h,k) is the center, r is the radius

7. the radius is the distance between the center and any point on the circle
__ using the distance formula, r^2=(-7-(-5))^2+(6-3)^2 __ r^2=13
__ so the equation is (x-3)^2+(y+5)^2=13

8. the center is the midpoint of the diameter __ ((10+2)/2,(-4+2)/2) __ (6,-1)
__ using the distance formula, r^2=(10-6)^2+(-4-(-1))^2 __ r^2=25
__ so the equation is (x-6)^2+(y+1)^2=25

9. the second and third points have the same y-coordinate, so a line connecting them is horizontal
__ the midpoint of the line has the same x-coordinate as the center of the circle __ (-5+7)/2=1, so the center is (1,y)

all radii of a circle are equal, so (distance formula again) __ (1-6)^2+(y-3)^2=(1-7)^2+(y-2)^2
__ 25+y^2-6y+9=36+y^2-4y+4 __ -2y=6 __ y=-3
__ using the distance formula, r^2=(1-(-5))^2+(-3-2)^2 __ r^2=61
__ so the equation is (x-1)^2+(y+3)^2=61
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