TANGENTS AND NORMALS WORKSHEET

(1)  Find the equations of the two tangents that can be drawn from (5, 2) to the ellipse 2x² + 7y² = 14.   Solution

(2)  Find the equations of tangents to the hyperbola (x²/16) - (y²/64)  =  1 which is parallel to 10x - 3y + 9  =  0.   Solution

(3)  Show that the line x − y + 4 = 0 is a tangent to the ellipse x²+ 3y² = 12 . Also find the coordinates of the point of contact.          Solution

(4)  Find the equation of the tangent to the parabola y² = 16x perpendicular to 2x + 2y + 3 = 0.  Solution

(5)  Find the equation of the tangent at t = 2 to the parabola y²= 8x . (Hint: use parametric form)    Solution

(6)  Find the equations of the tangent and normal to hyperbola 12x² − 9y² = 108 at θ  =  π/3 . (Hint : use parametric form)   Solution

(7)  Prove that the point of intersection of the tangents at ‘ t₁ ’ and ‘ t₂ ’on the parabola y² = 4ax is a t₁ t₂ , a(t₁ + t₂)     Solution

(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

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