v = (2x² – y² +4)i+(5y+3x – 6)j . Consider two closed paths starting (and ending) at a dock located at (-1,0): (1i) path 1: the triangle from (-1,0) to (2,0) to (0,2) and back to (-1,0). (ii) path 2: the circle of radius 1 centered at (0,0), traversed counter-clockwise; (ii) path 2: the circle of radius 1 centered at (0,0), traversed counter-clockwise; Which path would cause a rower to give more effort (i.e., produce a larger hindrance)? Is vector (velocity) field is conservative, I.e., is there a function f(x, y) such that Vƒ = v?

Q: Write the equation of a circle with centre (5, –2) which is tangent to the Y-axis. o (x + 5)² + (y –…

A: Here we have to write the equation of a circle with centre (5,-2) which is tangent to the y-axis.

Q: Determine the geometric location of the points in R3 that equidistant from the plane y = 3 and the…

A: This is question of 3d geometry and locus.

Q: If A ABC is reflected across the line y-z+ 1, what are the coordinates of Point A post-reflection?…

A: In the question it is asked to show the reflection of the triangle shown in figure. It is asked to…

Q: 3Q: If z₁ = 1.5 cisand z₂ = 4 cis(-7) find and express it in the rectangular form.

A:

Q: What is the distance from the point P=(2, -1, 4) to the plane 3x+5y-2z =20

A:

Q: Find the equation of the sphere having the circle x +y+ z2 = 9, x- 2y+ 2z = 5 as a great circle.

A: The solution is below.

Q: Find the equation of the circle which cuts the three circles…

A:

Q: 9. Find the equation for the plane through Po(-2,3,9) perpendicular to the line x = -2 – t, y = -3 +…

A:

Q: Write the standard equation of a circle with the center at (-1, -4) that passes through the point…

A:

Q: Find ∫C (2z + 9) / (z2 + 2z - 3) where C is the circle |z - 2| = 3.

A:

Q: Find the cosine of the angle between the planes -3x - 4y – 3z = 3 and the plane - 1x - 3y + 3z = -2.

A:

Q: Which equation represents a circle with a center at (2, - 7) and a radius of 4 units?

A:

Q: What is the equation of the circle n the ry-plane that has center (4,-5) and that passes through the…

A: Option 4 is correct.

Q: △ABC△ABC has vertices A(0,4), B(6,-1), and C(3,7). What are the coordinates of C' when the triangle…

A:

Q: Find the equation of a circle in standard form whose center is at (-4,3) and radius v5 * O…

A:

Q: Determine the point on the graph of z = x² + y²+ 10 closer to the plane x + 2y-z = 0

A:

Q: Find the x² + y² − 3x − 6y + 14 = 0, - equation of the circle which cuts th x² + y² − x − 4y + 8 = 0…

A: The circle having center at the radical center of the three given circles and radius equal to the…

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.