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)

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B

(0,12)

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C

(16,0)

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D

(0,0)

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Solution

## 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). ∴√(x−8)2+(y−6)2=10−−−−−(1) (∵ 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) (∵ X-coordinates of any point on y-axis is O) ⇒√0−82+(y−6)2=10 ⇒64+(y−6)2=102 ⇒(y−6)2=62 ⇒y−6=6 (or) y−6=−6 ⇒y=12 (or) y=0 ∴ Points where circle passes through Y-axis are (0,12) and (0,0) To find X-intercept put y =0 ⇒(x−8)2+62=102 ⇒(x−8)2=82 ⇒x−8=8 (or) x−8=−8 ⇒x=16 (or) x=0 ∴ Points where circle passes through X-axis are (16,0) and (0,0)

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