Question

if ab is diameter of circle c(O,r) where coordinates of a and b are (5,6) and (3,-2) respectively , then find the coordinates of O.

Answer 1

Step-by-step explanation:

Given:-

A circle with centre (2,−3) and AB is the diameter of circle with B(1,4).

To find:- Coordinate of point A.

Let (x,y) be the coordinate of A.

Since AB is the diameter of the circle, the centre will be the mid-point of AB.

now, as centre is the mid-point of AB.

x-coordinate of centre =

2

x+1

y-coordinate of centre =

2

y+4

But given that centre of circle is (2,−3).

Therefore,

2

x+1

=2⇒x=3

2

y+4

=−3⇒y=−10

Thus the coordinate of A is (3,−10).

Hence the correct answer is (3,−10).

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Answer 2

Answer:

(4,2)

Step-by-step explanation:

Concept= Radius and Diameter

Given= The Coordinates of diameter

To find= The Coordinates of radius

Explanation=

We have been the coordinates of diameter of circle and we need to find the radius coordinates.

The Diameter is AB.

Coordinates of A are (5,6)

Coordinates of B are (3,-2)

The coordinates of radius is O(x,y)

We know that radius is half of diameter.

Therefore the radius will be as

x= (5+3)/2 =8/2=4

y=(6-2)/2=4/2=2

The coordinates of O are(4,2)

Therefore the Coordinates of radius is (4,2)

The radius is the length between the coordinate of A and O

Radius = √(5-4)² + (6-2)²

Radius is √17 units

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