Geo5.1.12

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Find the vertex,latusrectum,axis,tangent at the vertex,focus and directrix of the parabola x^{2}-2x-4y-3=0\,

Given parabola is x^{2}-2x-4y-3=0\,

Rearranging the terms, we get

(x-2)^{2}=4(y+{\frac  {7}{4}})\,

Vetrex is (2,-{\frac  {7}{4}})\,

4a=4,a=1\,

Latusrectum is 4.

Focus is (2,{\frac  {-7}{4}}+1)=(2,-{\frac  {3}{4}})\,

Equation to the directrix is

y={\frac  {-7}{4}}-1,4y+11=0\,

Axis of the parabola is

x-2=0\,

Equation to tangent at vertex is y-{\frac  {7}{4}}=0,4y-7=0\,


Main Page:Geometry:The Parabola