FIND THE EQUATION OF CHORD OF CONTACT OF TANGENTS FROM THE POINT

When we take two distinct points P, Q on the parabola, we can join them to form a line segment called a chord. Sometimes we will refer to the line through P and Q as the chord.

To find equation of chord from the external point (x₁, y₁), we follow the rules given.

Find the equation to the chord of contact of tangents from the point.

Problem 1 :

(-3, 1) to the parabola y² = 8x

Solution :

y² = 8x

Equation of the parabola y² = 4ax

8x = 4ax

a = 2

yy₁ = 2a(x  + x₁)

(x₁, y₁) = (-3, 1)

y = 2(2)(x - 3)

y = 4(x - 3)

y = 4x - 12

4x - y - 12 = 0

Problem 2 :

(2, 4) to the ellipse 2x² + 5y² = 20

Solution :

Given equation is 2x² + 5y² = 20

2x² + 5y² - 20 = 0

2xx₁ + 5yy₁ - 20 = 0

Given point (2, 4) = (x₁, y₁)

2(2)x + 5(4)y - 20 = 0

4x + 20y  - 20 = 0

Dividing 4 on each sides.

x + 5y - 5 = 0

The required equation form is x + 5y - 5 = 0.

Problem 3 :

(5, 3) to the hyperbola 4x² - 6y² = 24

Solution :

Given, equation is 4x² - 6y² = 24

4x² - 6y² - 24 = 0

4xx₁ - 6yy₁ - 24 = 0

Given point (5, 3) = (x₁, y₁)

4(5)x - 6(3)y - 24 = 0

20x - 18y - 24 = 0

Dividing 2 on each sides.

10x - 9y - 12 = 0

The required equation form is 10x - 9y - 12 = 0.