Question

If the centre of a circle is ( − 2 , − 6 ) and the end points of its diameter are ( 1 , − 7 ) and ( x , − 5 ) , find the value of x .

Answer 1

Answer:

Let the coordinates of the one end of a diameter AB  of a circle are A(2,3) and B(x,y).

Let the coordinates of the center of the circle C(−2,5).

As center is the midpoint of the diameter AB so the coordinates of center is

C(22+x,23+y)

Now equating the coordinates of center we get

22+x=−2

⇒2+x=−4

⇒x=−4−2

⇒x=−6

23+y=5

⇒3+y=10

⇒y=10−3

⇒y=7

∴Coordinates of B=(−6,7).

Step-by-step explanation:

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