Find the equations of the tangents.
Problem 1 :
To the parabola y^{2} = 6x, parallel to 3x - 2y + 5 = 0.
Solution :
y^{2} = 6x
y^{2} = 4ax
6x = 4ax
6/4 = a
3/2 = a
Equation of tangent y = mx + a/m
Slope of the tangent = Slope of the line
= -(a/b)
= -(3/-2)
m = 3/2
So, equation of tangents is 3x - 2y + 2 = 0.
Problem 2 :
To the parabola y^{2} = 16x, perpendicular to the line 3x - y + 8 = 0.
Solution :
y^{2} = 16x
y^{2} = 4ax
16x = 4ax
16/4 = a
4 = a
Equation of tangent y = mx + a/m
Slope of the tangent = Slope of the line
= b/a
m = -1/3
So, equation of tangents is x + 3y + 36 = 0.
Problem 3 :
Solution :
Slope of the tangent = Slope of the line
= b/a
m = 1/1
m = 1
So, equation of tangents is x - y + 5 = 0.
Problem 4 :
To the hyperbola 4x^{2} - y^{2} = 64, which are parallel to 10x - 3y + 9 = 0.
Solution :
4x^{2} - y^{2} = 64
Equation of tangent y = mx + a/m
Slope of the tangent = Slope of the line
= -(a/b)
= -(10/-3)
m = 10/3
So, equation of tangents is 10x - 3y + 32 = 0.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM