Question

If a circle is drawn with centre C(4,0) and radius 6 cm as shown in below figure then find the coordinates of A and B.

• A. A =(10,0) b =(-2,0)
• B. A =(-2,0) b =(10,0)
• C. A =(10,0) B =(-1,0)
• D. Both a and b

Answer 1

The correct option is B

A =(-2,0) b =(10,0)

Given the centre of the circle 'C' =(4,0) and the radius is 6 cm.

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

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

$\Rightarrow \sqrt{(x-4{)}^2+(y-0{)}^2}=6--------\left(1\right)$

From the diagram we can see that 'A' and 'B' the points on X-axis.

$\therefore$ Put y=0 in eq (1)

$\Rightarrow \sqrt{(x-4{)}^2+0}=6$

$\Rightarrow (x-4{)}^2=6^2$

$\Rightarrow x-4=6$ (or) x-4 =-6

$\Rightarrow x=10\left(or\right)x=-2$

$\therefore$ Points are (10,0) and (-2,0)

$\therefore A=(-2,0)$ and B =(10,0)