Question

A circle of radius 10 units is drawn with (8,6) as the centre. At which of the given points does the circle pass through the co-ordinate axes?

• A. (0,2)
• B. (0,12)
• C. (16,0)
• D. (0,0)

Answer 1

Answer: (B), (C), (D)

The correct options are
B

(0,12)

C

(16,0)

D

(0,0)

Given the radius of the circle is 10 units. and the centre is (8,6).

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

$\therefore \sqrt{(x-8{)}^2+(y-6{)}^2}=10-----\left(1\right)$

$(\because$ distance from centre to any point on circle is equal to its radius)

To find coordinates where circle passes through Y-axis put x =0 in eq (1)

$(\because$ X-coordinates of any point on y-axis is O)

$\Rightarrow \sqrt{0-8^2+(y-6{)}^2}=10$

$\Rightarrow 64+(y-6{)}^2={10}^2$

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

$\Rightarrow y-6=6\left(or\right)y-6=-6$

$\Rightarrow y=12\left(or\right)y=0$

$\therefore$ Points where circle passes through Y-axis are (0,12) and (0,0)

To find X-intercept put y =0

$\Rightarrow (x-8{)}^2+6^2={10}^2$

$\Rightarrow (x-8{)}^2=8^2$

$\Rightarrow x-8=8\left(or\right)x-8=-8$

$\Rightarrow x=16\left(or\right)x=0$

$\therefore$ Points where circle passes through X-axis are (16,0) and (0,0)