Equation of Tangents from an External Point:

Let y² = 4ax be equation of a parabola and (x₁, y₁) an external point P. Then, equations of tangents from (x₁, y₁) to given parabola are given by

SS₁ = T², here S = y² - 4ax, S₁ = y₁² - 4ax₁, T = yy₁ - 2a(x + x₁)

Chord of Contact:

Equation to chord  of  contact of  the tangents  drawn  from  the  point  (x₁, y₁), to parabola  y²= 4ax is T= 0, that is yy₁ - 2a(x+x₁) =0.

Equation of a Chord with Midpoint (x₁, y₁):

The equation of chord of the parabola y²= 4ax having mid point (x₁, y₁) is T= S₁

i.e.    yy₁-2a(x+x₁)= y₁²-4ax₁ Or yy₁ - 2ax = y₁² - 2ax₁ .

Example: Find equation of chord of the parabola y² = 12x which is bisected at the point (5, -7).

Solution:        Here (x₁, y₁) = (5 -7) and y² = 12x, ∴a = 3

                        The equation of chord is S₁ = T

                        or y₁²- 4ax₁ = yy₁ - 2a (x + x₁)

                        or (-7)² - 12.5 = y(-7) - 6(x+5)

                        => 6x + 7y + 19 = 0.

Email based Equation of Tangents from an External Point Assignment Help - Homework Help

We at www.expertsmind.com offer email based Equation of Tangents from an External Point assignment help - homework help and projects assistance from k-12 school level to university and college level and engineering and management studies. We provide finest service of Mathematics assignment help and Mathematic homework help. Our experts are helping students in their studies and they offer instantaneous tutoring assistance giving their best practiced knowledge and spreading their world class education services through e-Learning program.

Expertsmind's best education services

• Quality assignment-homework help assistance 24x7 hrs
• Best qualified tutor's network
• Time on delivery
• Quality assurance before delivery
• 100% originality and fresh work