Geo5.1.14

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Find the equation of the normal to the parabola i).y^{2}=8x\, at (2,4)\, ii).y^{2}=4x\, at (1,2)\, iii).y^{2}=4x\, whose slope is 2

i).Given parabola is y^{2}=8x\,

a=2\,

m={\sqrt  {{\frac  {4+{\sqrt  {{\sqrt  {16-16}}}}}{4}}}}\,

m=1\,

y=x+{\frac  {2}{1}}\,

x-y+2=0\,

ii).y^{2}=2x\,

a={\frac  {1}{2}}\,

m={\sqrt  {{\frac  {2+{\sqrt  {4-4}}}{2}}}}\,

m=1\,

y=x+{\frac  {1}{2}}\,

2y-2x=0\,

x-y=0\,

iii). y^{2}=4x\,

a=1,m=2\,

y=2x+{\frac  {1}{2}}\,

2y-4x-1=0\,


Main Page:Geometry:The Parabola