# 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.

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