Question

The centre of a circle is at O(2x, x + 6). If the circle passes through the point (–7, 10) and has a diameter of

length 10 5 units, then find the coordinates of the centre of the circle​

Answer 1

hope that helps

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Answer 2

Given info : The centre of a circle is at O(2x, x + 6). If the circle passes through the point (–7, 10) and has a diameter of length 10√5 units.

To find : the coordinates of the centre of the circle is...

solution : we know, radius the minimum distance between centre and a point lying on the circumference of circle.

so radius = distance between (2x, x + 6) and (-7, 10)

diameter = 2 × distance between (2x, x + 6) and (-7, 10)

⇒10√5 = 2 × √{(2x + 7)² + (x + 6 - 10)²}

⇒5√5 = √{(2x + 7)² + (x - 4)²}

⇒125 = (2x + 7)² + (x - 4)²

⇒125 = 4x² + 28x + 49 + x² - 8x + 16

⇒60 = 5x² + 20x

⇒x² + 4x - 12 = 0

⇒x² + 6x - 2x - 12 = 0

⇒x(x + 6) - 2(x + 6) = 0

⇒(x - 2)(x + 6) = 0

⇒x = 2, -6

Therefore the values of x are 2 and -6.

so coordinates of circle are (4, 8) and (-12, 0)