Find the equation of the circle with diameter AB where A and B are the points (-1,2) and (3,3) respectively?

2 Answers
Sep 15, 2015

The answer could be find out by knowing some formulas of coordinate geometry.
1) standard eqn.=(xa)2+(yb)2=r2 (for this question i,e, radius)
2) midpoint= x1+x22,y1+y22
3) distance= (x2x1)2+(y2y1)2

Explanation:

we are given , A(-1,2) & B(3,3)
here x1= -1
y1= 2
x2= 3
y2= 3

Therefore, AB= (x2x1)2+(y2y1)2

= (3(1))2+(32)2

(4)2+(1)2

(16)+(1)

17.....................(Diameter)

so radius = 1/2 * diameter
= 17/2

now the radius can also be got by calculating the midpoint
so the next step is:
wkt,midpoint is given by =x1+x22,y1+y22

then,we get 1+32 , 2+32

= (22) , (52)

= (1 , 2.5)
Hence we get the values of a and b respectively.
Putting the values we get,
(xa)2+(yb)2=r2

= (x1)2+ (y2.5)2 = (17/2)2
= (x1)2+ (y2.5)2 = (174)
= (x1)2+ (y2.5)2 = 4.25
= (x1)2+ (y2.5)2 = 4.25........................(answer)

Sep 17, 2015

x2+y22x5y+3=0

Explanation:

Firstly, we can find the centre of the circle by finding the midpoint of AB. Since it the midpoint or the centre (h,k) cut AB with equal ratio;

Centre(h,k)=(1+32,2+32)

(h,k)=(1,52)

Then we can find the radius , r of the circle by using the equation;

r2=(xh)2+(yk)2

r=(xh)2+(yk)2

Substitute the coordinate (h,k)=(1,52) and any of A or B coordinates into equation. In this calculation I choose B.

r=(31)2+(352)2

r=174=172

To find c, we can use the equation c=h2+k2r2 and substitute (h,k)=(1,52) and r=172 into it.

c=(1)2+(52)2(172)2

c=3

Then we know that the equation of circle is known as;

x2+y22hx2ky+c=0

Substitute only (h,k)=(1,52) and c=3 and we get;

x2+y22(1)x2(52)y+3=0

x2+y22x5y+3=0