Question

If a circle is drawn with centre c(4,0) and radius 5 cm as shown in the below figure then find the coordinates of 'R' and 'S'.

• A. R=(0,5) and S=(0,-5)
• B. R =(3,-3) S =(0,3)
• C. R =(0,3) S =(0,-3)
• D. R =(0,-5), S=(0,5)

Answer 1

The correct option is C

R =(0,3) S =(0,-3)

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

$\because$ Distance between centre and any point on circle is equal to radius of the circle.

let p (x,y) be a point on circle

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

From the given diagram points 'R' and 'S' are on Y-axis.

$\therefore$ Put x=0 in above equation

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

$\Rightarrow y^2+4^2=5^2$

$\Rightarrow y^2=5^2-4^2$

$=3^2$

$\Rightarrow y=\pm 3$

$\therefore$ Points are (0,3) (0,-3)

$\therefore$ R =(0,3) and S=(0,-3)