Question

the radius of circle passing through the point 6,2 and whose two diameters are x+y=6 and x+2y=4 is

Answer 1

A diameter of a circle always passes through its centre.
From the above statement we can find the centre of circle by solving the equations of diameter simultaneously.

$(x + y = 6) \times 2 \\ 2x + 2y = 12$
equation 1

$x + 2y = 4$
equation 2

Subtracting equation 2 from equation 1 we get
$2x + 2y = 12 \\ - (x + 2y = 4)$
$x = 8 \\ y = - 2$
Therefore the centre of circle is (8, -2)

Radius is the distance from centre to its perimeter.
It is given that the circle passes through (6, 2)
Therefore radius is the distance between these two points
using distance formula;

Radius =
$\sqrt{ (6 - 8) ^{2} + (2 - ( - 2)) ^{2} } = \sqrt{20}$

Answer 2

Answer:A diameter of a circle always passes through its centre.

From the above statement we can find the centre of circle by solving the equations of diameter simultaneously.

equation 1

equation 2

Subtracting equation 2 from equation 1 we get

Therefore the centre of circle is (8, -2)

Radius is the distance from centre to its perimeter.

It is given that the circle passes through (6, 2)

Therefore radius is the distance between these two points

using distance formula;

Radius =

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