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y^2+2y-x+5=0 represents a parabola. Find...

`y^2+2y-x+5=0` represents a parabola. Find its vertex, equation of axis, equation of latus rectum, coordinates of the focus, equation of the directrix, extremities of the latus rectum, and the length of the latus rectum.

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To solve the equation \(y^2 + 2y - x + 5 = 0\) and find the properties of the parabola, we will follow these steps: ### Step 1: Rewrite the equation in standard form Start by rearranging the equation to isolate \(x\): \[ y^2 + 2y = x - 5 \] Now, complete the square for the \(y\) terms: ...
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