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- What are the tangent and normal line equations of the parametric curve in the figure at the point t = 0?Find a parametric equation for the line that is perpendicular to the graph of the equation 4x^2 + 2y^2 +3z^2 = 39 at the points (1,2,3). Use t as the variableFind the unit vectors that are parallel to the tangent line to the parabola y = x^2 at point (2, 4). Attached is a picture of the problem. Thank you.
- Find equations of all tangents to the parametric curve that pass through the point (4, 3). In entering your answer, list the equations starting with the smallest slope. If two or more tangent lines share the same slope, list those lines starting with the smallest y-intercept. If an answer field is not used, type an upper-case "N" in that blank. Tangent line 1: y = Tangent line 2: y = x = 3t² + 1, y = 2t³ + 1 Tangent line 3: y =Explain Directional Derivatives and Gradient VectorsFind the parametric equation to describe the following curve: b) the part of x = 2y^2 - 1 from (-1,0) to (7,2)
- Let L be the line with parametric equations x = 1-t y = 3-3t z = t Find the vector equation for a line that passes through the point P=(-10,-7, 2) and intersects L at a point that is distance 5 from the point Q-(1, 3, 0). Note that there are two possible correct answers. Use the square root symbol '' where needed to give an exact value for your answer. X SN 0 0+t0 0Give a vector parametric equation for the line through the point (4,-3) that is perpendicular to the line <1−4t,3t−3>Find point (2, 1, 8) an equation for the tangent plane to z -x² - y° = 3 at the