Question

Please help!!!
Write the equation of the circle that satisfies this condition: The endpoints of a diameter are at (-2,-3) and and at (4,5)

Answer 1

@ParthKohli @ganeshie8 @Hero @dan

Answer 2

If you have the endpoints of the diameter of a circle, the center of the circle can be found using the midpoint formula, correct?

Answer 3

(x+2)(x-4)+(y+3)(y-5)=0

Answer 4

is that x1+x2/2 and y1+y2/2?

Answer 5

i got (1,1)

Answer 6

yes

Answer 7

(x+2)(x-4)+(y+3)(y-5)=0 is the required equation

Answer 8

Very good. Now find the radius. The radius is the length from one of the endpoints to the center point of the circle.

Answer 9

if the ends of diameter have coordinates (a,b) and (c,d ) then equation of circle is (x-a)(x-c)+(y-b)(y-d)=0

Answer 10

so can I use (1,1) and (4,5)? the distance between these?

Answer 11

@Hero

Answer 12

Yes, you can use the distance formula to find the distance between those two points.

Answer 13

Afterwards you'll have the radius \(r\) and the center \((h,k)\). From there, you can insert those values in to the equation of a circle:

\((x - h)^2 + (y - k)^2 = r^2\)

Answer 14

so radius is 5? or is it 5 squared?

Answer 15

You calculated r already? Can you show please the work you did to calculate \(r\) if you don't mind?

Answer 16

That looks good. So what do you believe is the equation of the circle?

Answer 17

The the left side is equal to \(r^2\) not just \(r\).

Answer 18

so its 25

Answer 19

So the equation of the circle is...?

Answer 20

\[(x-1)^{2}+(y-1)^{2}=25\]

Answer 21

Excellent work.

Answer 22

Thank you for your help!!!