Which of the following is true about the pathway of the graph for the parametric equations belov æ(t) = -3t + 3, y(t) = VE – 2 O Astincreases, x increases and y increases Astincreases, x decreases and y increases Astincreases, x decreases and y decreases O Astincreases, x increases and y decreases

Q: 8. Find the equation of the parabola ax? + by? + cxy + dx + ey nat passes through the points (3, 1),…

A: A parabola is given by, ax2+by2+cxy+dx+ey+f=0. Also the parabola passes through the points 3,1 and…

Q: Which of the following functions do not form a set of fundamental solutions of y" - 4y = 0 Select…

A: We have to convert them into general characteristics equation, (D2-4)y=0 Where D = ddt and D2 is…

Q: Prove that the equation S =x+4xy+3y²– 4x – 10y +3=0 represents a pair of lines and find the…

A: Given equation is  S≡x2+4xy+3y2-4x-10y+3=0.   Since, the general equation  ax2+2hxy+by2+2gx+2fy+c=0…

Q: Identify and sketch the graph of the following equations in R³ (a) x2 + 4y² + z² – 8x + 16y – 2z +…

A: we can add or subtract same amount from a equation to simplify equation. The logarithm function…

Q: 7. A curve in the zy-plane is described by the equation 2y(x − 1)² – xy² + 1 = 0. (a) Determine…

A: Given equation of curve: 2yx-132-xy2+1=0 Now, from the given points (1,0) , (2,0), (1,1) , (2,1) and…

Q: Find the coordinates of the intersection points A and B, between the closed curve (x + 1)² + 4(y-1)²…

A: In this question, we can find the intersection points of the given curve. Using the equation of…

Q: Write each system in matrix form- = Ax. dx dt Determine the eigenvalues of A. State whether the…

A:

Q: 2. The general form of a cubic is p(x) = ao + a1x +a2x² + a3x³ %3D Suppose you are given the…

A: What we basically need to do in this question is interpolation which can be done by various methods,…

Q: 3x - 2y + 4z 8x + y - 9z passes through the point (-7, -2, 5). Solve your equation for z. Suppose…

A:

Q: #8 8. Write an equation of a line passing through the point (4, -9) and parallel to the line 3x — 6у…

A:

Q: 4. Name the coordinates of the image of Q(-2, 5) under a translation along (x, y) → (x + 5, у - 3).

A: We have to find the name the coordinates of the image of Q(-2,5) under a translation along…

Q: 1. Determine the order of the following DEs and whether it is linear or not. (a) y(3)+2x = y (b) y"…

A:

Q: 2. Let C₁ be the ellipse + 4 16 = 1 traced counterclockwise and C₂ be the triangle with vertices at…

A:

Q: 7. On a certain mountain range, the level is z = 1200 -0.02x² -0.04y². points north. The climber is…

A:

Q: The function of f(y) is a "sideways" parabola with a standard equation of SW) = ay² + by + c, f(G)…

A: Given: Focus of Parabola:  (2, 6) Equation of Directrix:  x = -15

Q: Which of the following defines an equation of a plane curve that does NOT have a vertical asymptote?…

A: Given:  We have to find the equation of plane curve which has no vertical asymptote.

Q: 3. When origin is shifted to (3,4) by translation of axes, find the transformed equation of 2x² +…

A: We have to solve given problems:

Q: xe" + ye" = a e* + ey + eu + ev = b Find all points (x, y, u, v) at which no pair of the variables…

A: We will use the generalized inverse function Theorem, to find the set of non-differentiable points…

Q: ) Find of the implicit function a? + 5xy + y? – 2x + y – 6 = 0 at the point 1. . (1, 1).

A: Topic:- derivatives

Q: The equation of a quadratic relation is y = -(x - 1)² +3. Every point on this conic is equidistant…

A:

Q: For the equation ay" + by' + cy = 0, if b² – 4ac 0 (the repeated %3D Y1 e-bt/2a and the second…

A:

Q: Theorem 1. Assume that B(y + 38) < (1 – a)(y+ 8)² and a< 1. - Then the equilibrium point of Eq.(1)…

A: Note:- In given proof, provided by you in pictures, c and d is written, it is misprint.  From…

Q: Solve for y. e+ 0.5y 1.5 #-2 2-3 1/7

A: Given,    x+0.5y=1.5

Q: E(x) = 2x-3 X-2 %3D Graph rational funcHons. Using transcormaHons. nLe State Domoin arange. と(-

A: Given Rational function r(x)=(2x-3)/(x-2) We need to use transform of the graph y=1/x

Q: 4. The line Ly passes through the points (1,1,-1) and (4-3,0) and the line L2 has the equation L2:…

A: Step 1:Step 2:Step 3: Step 4:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.