4 unit Chord of Contact in Conics (1 Viewer)

[murraysp]

Find the equation of the chord of contact of tangents from the point (5,4) to the ellipse (x^2)/15 + (y^2)/10 = 1

Thank you.

 

[Ferox]

Equation of a chord of contact from T(x_o, y_o) is

x_ox/a² + y_oy/b² = 1

Therefore for x²/15 + y²/10 = 1 from (5,4)

5x/15 + 4y/10 = 1
x/3 + 2y/5 = 1



EDIT: I'm not sure if you're supposed to derive that equation.

If you are, you note that from T(x_o, y_o) two tangents can be drawn
Tangent at P(x₁, y₁): x₁x/a² + y₁y/b² = 1, and
Tangent at Q(x₂, y₂): x₂x/a² + y₂y/b² = 1

T lies on both tangents, therefore
x₁x_o/a² + y₁y_o/b² = 1, and
x₂x_o/a² + y₂y_o/b² = 1

Therefore the chord through both tangents is x_ox/a² + y_oy/b² = 1

 

[Sakeeee]

if they say find then just take your chord of contact and sub in x0,y0 WHICH THEY ALWAYS GIVE YOU. yeah it's very confusing cause it seems too fucking easy.

THE ONLY HARD THING IN CHORD OF CONTACTS IS PROVING IT! OTHERWISE IT'S A JOKE