Geo5.1.13

From Example Problems
Jump to: navigation, search

Find the equation of the tangent to the parabola i)y^{2}=16x\, inclined at 60 degrees to X-axis. ii).y^{2}=8ax\, at (2a,4a)\,

i).parabola is y^{2}=16x\,

a=4,m=\tan 60^{\circ }={\sqrt  {3}}\,

Equation of the tangent is

y={\sqrt  {3}}x+{\frac  {4}{{\sqrt  {3}}}}\,

{\sqrt  {3}}y=3x+4\,

ii).Given parabola is y^{2}=8ax\,

a=2a\,

m={\sqrt  {{\frac  {4a+{\sqrt  {16a^{2}-16a^{2}}}}{4a}}}}\,

m=1\,

Equation of the tangent is

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

y=x+2a\,


Main Page:Geometry:The Parabola