Question

If a circle is drawn with centre C(0,4) and a radius of 5 cm as shown in below figure then find the coordinates of A and B.

• A. A =(0,9) B=(0,1)
• B. A =(0,-1) B=(0,9)
• C. A =(0,9) B=(0,-1)
• D. A =(0,1) B=(0,9)

Answer 1

The correct option is C

A =(0,9) B=(0,-1)

Given the centre of circle 'C' =(0,4) and the radius is 5 cm.

Now to any point on the circle the distance from centre is equal to the radius of the circle

Let P(x,y) be a point on the circle

$\Rightarrow \sqrt{(x-0{)}^2+(y-4{)}^2}=5$

From the given diagram we can see A and B are points on Y-axis.

$\therefore$ put x=0 in the above equation

$\Rightarrow \sqrt{(y-4{)}^2}=5$

$\Rightarrow (y-4{)}^2=5^2$

$\Rightarrow y-4=5\left(or\right)y-4=-5$

$\Rightarrow y=9\left(or\right)y=-1$

$\therefore$ Points are (0,9) and (0,-1)

$\therefore$ A =(0,9) and B =(0,-1)