Question

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

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

Answer 1

The correct option is B

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

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

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

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

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

From the diagram we can see R and S are the points on the X-axis.

$\therefore$ put y =0 in the above equation.

$\Rightarrow \sqrt{x^2+4^2}=5$

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

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

$=3^2$

$\Rightarrow x=\pm 3$

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

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