Problem 1 :
Find the equation of the two tangent can be drawn from (5, 2) to the ellipse 2x^{2} + 7y^{2} = 14
Problem 2 :
Find the equations of tangents to the hyperbola
which are parallel to 10x - 3y + 9 = 0
Problem 3 :
Show that the line x - y + 4 = 0 is a tangent to the ellipse
x^{2} + 3y^{2} = 12
Also find the coordinate of the point of contact.
Problem 4 :
Find the equation of the tangent to the parabola y^{2} = 16x perpendicular to 2x + 2y + 3 = 0
Problem 5 :
Find the equation of the tangent at t = 2 to the parabola y^{2} = 8x
Problem 6 :
Find the equations of tangent and normal to hyperbola 12x^{2} - 9y^{2} = 108 at θ = π/3
Problem 7 :
Prove that the point of intersection of the tangents at t_{1} and t_{2} on the parabola y^{2} = 4ax is (at_{1} t_{2}, a(t_{1} + t_{2}))
Problem 8 :
If the normal at the point t_{1} on the parabola y^{2} = 4ax meets the parabola again at the point t_{2} , then prove that
t_{2} = -(t_{1} + 2/t_{1})
1) x - 9 y + 13 = 0 and x - y + 3 = 0
2) 10x - 3y + 32 = 0 and 10x - 3y - 32 = 0
3) So, the given line is tangent to the given ellipse
4) y = x + 4
5) x - 2y + 8 = 0
6) So, equation of tangent is 4x - 3y = 6 and normal is 3x + 4y = 42.
7) Point of intersection is (a t_{1}t_{2, }a(t_{1 }+ t_{2})).
8) t_{2 }= -(2/t_{1} + t_{1})
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM