Question

A circle of radius 5 units in the XY plane has its centre in the first quadrant, touches the X-axis and has a chord of length 6 units on the Y-axis. The coordinates of its centre are


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Answer 1

Given : Circle of radius 5 units in the XY plane has its centre in the first quadrant, touches the X-axis and has a chord of length 6 units on the Y-axis.

To Find :  The coordinates of its centre are

Solution:

radius 5 units in the XY plane has its centre in the first quadrant,

touches the X-axis => y coordinate of center = 5

so center  O = ( x , 5 )

a chord of length 6 units on the Y-axis.

AB = 6 cm

AB/2 = 3  cm

=> AM = 3 cm

OA² - AM² = OM²

=> 5² - 3² = OM²

=> OM² = 16

=> OM = 4

The coordinates of its centre are ( 4 , 5)

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Answer 2

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(4,5)