EXERCISE 5.4

EXERCISE . . Find the equations of the two tangents that can be drawn from ( , ) to the ellipse . Find the equations of tangents to the hyperbola x = which are parallel to = . . Show that the line x is a tangent to the ellipse x . Also find the coordinates of the point of contact. - - Two Dimensional Analytical Geometry - II . Find the equation of the tangent to the parabola y perpendicular to2 . Find the equation of the tangent at t = 2to the parabola y . (Hint: use parametric form) . Find the equations of the tangent and normal to hyperbola at θ = . (Hint: use parametric form) . Prove that the point of intersection of the tangents at ‘ t ’ and ‘ t ’on the parabola y ax is at t a t   . . If the normal at the point ‘ t ’ on the parabola y ax meets the parabola again at the point ‘ t ’, then prove that t   .