Problem 1 :
Find the equations of the tangents to the parabola y2 = 5x from the point (5, 13). Also find the points of contact.
Problem 2 :
Find the equation of the two tangents that can be drawn
From the point (2, -3) to the parabola y2 = 4x.
Problem 3 :
Find the equation of the two tangents that can be drawn
(i) From the point (2, -3) to the parabola y2 = 4x.
(ii) From the point (1, 3) to the ellipse 4x2 + 9y2 = 36.
(iii) From the point (1, 2) to the hyperbola 2x2 - 3y2 = 6.
1) 2y = 5x + 1 and 10y = x + 125, the points of contact are (1/5, 1), (125, 25).
2) x + y + 1 = 0
3) i) x + y + 1 = 0
ii) 5x + 4y - 17 = 0
iii) 3x + y - 5 = 0
Problem 1 :
Find the equation of the two tangent can be drawn from (5, 2) to the ellipse 2x2 + 7y2 = 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
x2 + 3y2 = 12
Also find the coordinate of the point of contact.
Problem 4 :
Find the equation of the tangent to the parabola y2 = 16x perpendicular to 2x + 2y + 3 = 0
Problem 5 :
Find the equation of the tangent at t = 2 to the parabola y2 = 8x
Problem 6 :
Find the equations of tangent and normal to hyperbola 12x2 - 9y2 = 108 at θ = π/3
Problem 7 :
Prove that the point of intersection of the tangents at t1 and t2 on the parabola y2 = 4ax is (at1 t2, a(t1 + t2))
Problem 8 :
If the normal at the point t1 on the parabola y2 = 4ax meets the parabola again at the point t2 , then prove that
t2 = -(t1 + 2/t1)
1) x - 9y + 13 = 0, x - y + 3 = 0
2) 10x - 3y + 32 = 0, 10x - 3y - 32 = 0
3) it is the tangent
4) y = x + 4
5) x - 2y + 8 = 0
6) equation of tangent is 4x - 3y = 6 and normal is 3x + 4y = 42.
7) Point of intersection is (a t1t2, a(t1 + t2)).
8) t2 = -(2/t1 + t1)
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM