Write the equation of a circle who's diameter has endpoints (6,-5) and (2,1)

(x+1)

2

+(y−1)

2

=13

Explanation:

The standard form of the equation of a circle is .

(x−a)

2

+(y−b)

2

=r

2

​

where (a,b) are the coordinates of the centre and r, the radius.

To establish the equation, we required to know it's centre and radius.

Since we are given the endpoints of the diameter. Then the centre will be at the midpoint and the radius will be the distance from the centre to either of the 2 endpoints.

The midpoint can be calculated using the midpoint formula.

2

1

​

(x

1

​

+x

2

​

),

2

1

​

(y

1

​

+y

2

​

)

​

where (x

1

​

,y

1

​

) and (x

2

​

,y

2

​

) are points

The 2 points here are (−2,3) and (4,−1)

⇒ centre =(

2

1

​

(−2+4),

2

1

​

(3−1))=(1,1)

To calculate the radius use the distance formula

r=

(x

2

​

−x

1

​

)

2

+(y

2

​

−y

1

​

)

2

​

​

where (x

1

​

,y

1

​

) and (x

2

​

,y

2

​

) are 2 points

The 2 points here are the centre (1,1) and the endpoint (−2,3)

r=

(−2−1)

2

+(3−1)

2

​

=

9+4

​

=

13

​

The equation of the circle can now be written.

(x−1)

2

+(y−1)

2

=(

13

​

)

2

⇒(x−1)

2

+(y−1)

2

=13 is the equation of the circle

Step-by-step explanation:

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5

answer:

c. the third graph