A curve given parametrically by (x, y, z) = (1 + 3t, 2 − 3t², −3t+ 3t³). There is a unique point P on the curve with the property that the tangent line at P passes through the point (-17, -79, -306). The point P has coordinates ( · ).

Q: Suppose XY has coordinates X( -2, 5) and Y(3, -9). What are the coordinates for the midpoint of XY?

A: To find the Midpoint of the line.

Q: Find the distance between two points (1, 2) and (3, −1).

A: We want to find the distance between the given two points. We use formula for finding the distance…

Q: Find the midpoint of points A(-8,2)and B(-5,-5) graphically.

A: Explanation: Plot the points A and B on the graph. Then draw a horizontal line from A and Vertical…

Q: Find parametric equations for the line of slope 6 that passes through the point (7,9). (Use t as…

A:

Q: Find the distance d between the points (1, 3) and (5, 6).

A: Our Aim is to find the distance between the points (1,3) and (5,6).

Q: Draw a diagram showing two perpendicular lines that intersecton the -axis and are both tangent to…

A: The given parabola equation , y=x2. To draw two perpendicular lines that intersect on the axis and…

Q: Find parametric equations for the line of slope 2 that passes through the point 13, 52 .

A: Equation of line in the parametric form form when it is passes through point x1,y1 and slope 'r' is…

Q: Through the point (2, -4, 0) and parallel to each of the planes 2x + y -z = 0 and x+ 5y + 3z = 0.

A:

Q: a circle is tangent to the line 2x-y+1=0 at the point (2,5) and the center is on the line x+y=9.…

A: Given that Line 2x-y+1=0 touches the circle at point P(2,5). It means line passes through P(2,5) and…