Question 895413
The centre of a circle is (2x-1, 3x + 1). Find x if the circle passes through (-3,-1) and the length of its diameter is 20 unit.
<pre>
Center-radius equation of a circle: {{{(x - h)^2 + (y - k)^2 = r^2}}}, with:
(x, y) being:  ({{{- 3}}}, {{{- 1}}})
(h, k) being:  ({{{2x - 1}}}, {{{3x + 1}}}), and
r, or radius being: 10
{{{(x - h)^2 + (y - k)^2 = r^2}}} becomes: {{{(- 3 - (2x - 1))^2 + (- 1 - (3x + 1))^2 = 10^2}}}____Substituting values into center-radius equation of a circle
{{{(- 3 - 2x + 1)^2 + (- 1 - 3x - 1)^2 = 10^2}}}
{{{(- 2x - 2)^2 + (- 3x - 2)^2 = 10^2}}}
{{{4x^2 + 8x + 4 + 9x^2 + 12x + 4 = 100}}}
{{{4x^2 + 9x^2 + 8x + 12x + 4 + 4 - 100 = 0}}}
{{{13x^2 + 20x - 92 = 0}}}
{{{13x^2 + 46x - 26x - 92 = 0}}}
{{{x(13x + 46) - 2(13x + 46) = 0}}}
{{{(x - 2)(13x + 46) = 0}}}
{{{highlight_green(highlight_green(x = 2))}}}         OR        {{{highlight_green(highlight_green(x = - 46/13))}}}
You can do the check!! 

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