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 (x_{1}, y_{1}), 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 y^{2} = 8x
Solution :
y^{2} = 8x
Equation of the parabola y^{2} = 4ax
8x = 4ax
a = 2
yy_{1} = 2a(x + x_{1})
(x_{1}, y_{1}) = (-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 2x^{2} + 5y^{2} = 20
Solution :
Given equation is 2x^{2} + 5y^{2} = 20
2x^{2} + 5y^{2} - 20 = 0
2xx_{1} + 5yy_{1} - 20 = 0
Given point (2, 4) = (x_{1}, y_{1})
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 4x^{2} - 6y^{2} = 24
Solution :
Given, equation is 4x^{2} - 6y^{2} = 24
4x^{2} - 6y^{2} - 24 = 0
4xx_{1} - 6yy_{1} - 24 = 0
Given point (5, 3) = (x_{1}, y_{1})
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.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM