# EQUATION OF TANGENT FROM EXTERNAL POINT WORKSHEET

Problem 1 :

Find the equations of the tangents to the parabola y2 = 5x from the point (5, 13). Also find the points of contact.

Solution

Problem 2 :

Find the equation of the two tangents that can be drawn

From the point (2, -3) to the parabola y2 = 4x.

Solution

Problem 3 :

Find the equation of the two tangents that can be drawn

(i)  From the point (2, -3) to the parabola y2 = 4x.

Solution

(ii)  From the point (1, 3) to the ellipse 4x2 + 9y2 = 36.

Solution

(iii)  From the point (1, 2) to the hyperbola 2x2 - 3y2 = 6.

Solution

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

Solution

Problem 2 :

Find the equations of tangents to the hyperbola

which are parallel to 10x - 3y + 9 = 0

Solution

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.

Solution

Problem 4 :

Find the equation of the tangent to the parabola y2 = 16x perpendicular to 2x + 2y + 3 = 0

Solution

Problem 5 :

Find the equation of the tangent at t = 2 to the parabola y2 = 8x

Solution

Problem 6 :

Find the equations of tangent and normal to hyperbola 12x2 - 9y2 = 108 at θ = π/3

Solution

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))

Solution

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)

Solution

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(t+ t2)).

8)  t= -(2/t1 + t1)

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