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The circle x^2+""y^2=""4x""+""8y""+""5 i...

The circle `x^2+""y^2=""4x""+""8y""+""5` intersects the line `3x""""4y""=""m` at two distinct points if (1) ` 35""<""m""<""15` (2) `15""<""m""<""65` (3) `35""<""m""<""85` (4) ` 85""<""m""<"" 35`

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To solve the problem, we need to determine the conditions under which the line \(3x - 4y = m\) intersects the circle given by the equation \(x^2 + y^2 = 4x + 8y + 5\) at two distinct points. ### Step 1: Rewrite the Circle Equation First, we rewrite the equation of the circle in standard form. Starting with: \[ x^2 + y^2 - 4x - 8y - 5 = 0 ...
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