Question

If a circle is drawn with centre 'C' (0,8) and radius 10 cm as shown in figure then find the coordinates of R and S.

Answer 1

Given the centre of circle 'C' =(0,8) and radius =10 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.

$\Rightarrow \sqrt{(x-0{)}^2+(y-8{)}^2}=10$

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

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

$\Rightarrow \sqrt{x^2+8^2}=10$

$\Rightarrow x^2+8^2={10}^2$

$\Rightarrow x^2={10}^2-8^2$

$=6^2$

$\Rightarrow x=\pm 6$

$\therefore$ Points are (6,0) and (-6,0)

$\therefore$ R =(6,0) and S =(-6,0)