Question

If a circle is drawn with centre 'C' (0,5) and radius 13 cm as shown in figure, then the coordinates of R and S are___

• A. R=(-12,0)
  S=(12,0)
• B. R=(-5,0)
  S=(5,0)
• C. R=(5,0)
  S=(-5,0)
• D. R=(12,0)
  S=(-12,0)

Answer 1

The correct option is D

R=(12,0)
S=(-12,0)

Given the centre of circle 'C' =(0,5) and radius =13 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.

$\Rightarrow \sqrt{(x-0{)}^2+(y-5{)}^2}=13$

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

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

$\Rightarrow \sqrt{x^2+5^2}=13$

$\Rightarrow x^2+5^2={13}^2$

$\Rightarrow x^2={13}^2-5^2$

$={12}^2$

$\Rightarrow x=\pm 12$

$\therefore$ Points are (12,0) and (-12,0)

$\therefore$ R =(12,0) and S =(-12,0)