# On the coordinate plane , points P and B are defined by the coordinates (-1,0) and (3,3), ...

On the coordinate plane , points P and B are defined by the coordinates (-1,0) and (3,3), respectively, and are connected to form a chord of a circle which also lies on the plane. If the area of the circle is (25/4) π , what are the coordinates of the center of the circle ?

## Answer/Solution

(1,1.5)

### Steps/Work

Although it took me 3 mins to solve this question using all those equations, later I thought this question can be solved easily using options.

One property to keep in mind - A line passing through the centre of the circle bisects the chord (or passes from the mid point of the chord).

Now mid point of chord here is (-1+3)/2, (3+0)/2 i.e. (1,1.5) now luckily we have this in our Ans. choice. so definitely this is the ans. It also indictaes that PB is the diameter of the circle.

There can be a case when PB is not a diameter but in that case also the y-coordinate will remain same as it is the midpoint of the chord and we are moving up in the st. line to locate the centre of the circle.

If ans choices are all distinct (y cordinates) ONLY CHECK FOR Y CORDINATE and mark the ans=D

One property to keep in mind - A line passing through the centre of the circle bisects the chord (or passes from the mid point of the chord).

Now mid point of chord here is (-1+3)/2, (3+0)/2 i.e. (1,1.5) now luckily we have this in our Ans. choice. so definitely this is the ans. It also indictaes that PB is the diameter of the circle.

There can be a case when PB is not a diameter but in that case also the y-coordinate will remain same as it is the midpoint of the chord and we are moving up in the st. line to locate the centre of the circle.

If ans choices are all distinct (y cordinates) ONLY CHECK FOR Y CORDINATE and mark the ans=D