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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).

(x8)2+(y6)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)

082+(y6)2=10

64+(y6)2=102

(y6)2=62

y6=6 (or) y6=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

(x8)2+62=102

(x8)2=82

x8=8 (or) x8=8

x=16 (or) x=0

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


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