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

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