12 marks] 8. Find the equations of both the tangent lines to the hyperbola x? -...
1. (10 pts.) Find the equations of the two tangent lines to the parametric curve x = 1, y = 2 - 81 at the point (4,0).
Let f(x) = x². There are two lines with positive slope that are tangent to the parabola and that pass through the point (5, 22.75). Find the equation of the line with the smaller slope.
Find equations of the tangent lines to the curve y = (x-1)/(x+1) that are parallel to the line x − 2y = 5.
3. Find the equations of tangent and normal lines to the given curves at the given points. y2 – 2x – 4y - 1 = 0, at the point (-2,1).
please answer both (12(8 pts) Find parametric equations of the line through the point (2, -1,3) and perpendicular to the line with parametric equations 1-t,y 4- 2t and 3+ t and perpendicular to the line with parametric equations 3+t,y 2-t and z 3+2t. (13)(8 pts) Find the unit tangent vector (T(t) for the vector function r(t) - costi+3t j+ 2sin 2t k at the point where t 0 (12(8 pts) Find parametric equations of the line through the point (2,...
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or skew. If they intersect, find the point of intersection Given SI: x2-2y2 = 4z2-252 &s2: (0 Show that the tangent planes to the two surfaces at P(2,0,-8) are perpendicular. whether the lines parallel, 2-z & 12 Marks] 4x2 +9y2-24. (B) Find the points on Si at which the tangent plane is parallel to the plane x+y+32-5 3 Marks] Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or...
#1 Find the slope and the equations of the tangent lines to the given curves at each of the given points. 1. x= 2 cos e y = 3 sin TT a. r = 4 7T b. 2 2. x = cos 20 y = sin 40 TT a. r = 4 TC 2 b. r=
There are two lines through the point (-1,5) that are tangent to the parabola f(x)=x^2-2x. Find the x-coordinates of the points where these lines touch the parabola.
1. (10 pts.) Find the equations of the two tangent lines to the parametric curve r = y = 20 - 81 at the point (4,0).
(a) Find the slope m of the tangent to the curve y = 2 + 4x2 − 2x3 at the point where x = a. m = (b) Find equations of the tangent lines at the points (1, 4) and (2, 2). y(x) = (at the point (1, 4)) y(x) = (at the point (2, 2)) (c) Graph the curve and both tangents on a common screen. say and the sose m of the target to the survey * 2...