Question

the abscissae of two points A and B are roots of equation x^2 + 2ax - 4 = 0 and their ordinates are roots of equation x^2 + 2bx -9 =0. then equation of circle with AB as diameter is​

Answer 1

$\underline{\underline{\mathfrak{\Large{Solution : }}}}\\ \\ \sf\: Let\: A\: and \: B\: be\: (x_{1},y_{1}), (x_2,y_2). \\ \\ \sf\: x_1 \:and\: x_2 \: are\:roots\:of\: x^2 + 2ax - 4 = 0 \\ \\ \sf\: Then\: x_1 + x_2 = - 2a, x_1x_2 = - 4 \\ \\ \sf\:y_1, y_2\: are\: roots\: of\: x^2 + 2bx - 9 = 0 \\ \\ \sf\: Equation\:of\:circle\:on\:AB\:as\:diameter \: is \\ \\ \sf\: (x - x_1)(x - x_2) + (y - y_1)(y - y_2) = 0 \\ \\ \sf\implies\: x^2 + y^2 + 2ax + 2by - 13 = 0$

Answer 2

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