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Find the vertex, focus and directrix of the parabola `x^(2)=2(2x+y)`. |
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Answer» Correct Answer - `"Vertex"-=(2,-2),"Focus"-=(2,-3//2),"Directrix":y=-(5)/(2)` We have `x^(2)=2(2x+y)` `:." "x^(2)-4x+4=2(y+2)` `rArr" "(x-2)^(2)=2(y+2)` Comparing with `(x-h)^(2)=2(y-k)`, we get Vertex of the parabola is (2,-2). Length of latus rectum =4a=2 Axis of the parabola is x=2. Also, parabola is concave upward. Focus lies at distance a units above the vertex on the axis. So, focus is `(2,-2+(1)/(2))-=(2,-(3)/(2))`. Directrix is at distance a units below the vertex and perpendicular to the axis. Therefore, directrix is `y=-2-(1)/(2)ory=-(5)/(2)`. |
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