Find the rectangular coordinates of the pair of points (6, π) and (5, 7π/4). Then find the distance, in simplified radical form, between the points.

Q: Convert (2,-pi/6) into its rectangular coordinates

A: We can solve this as follows:

Q: The standard form of the equation of a circle with center (h, k) and radius r is

A: Consider the given information. The center of the circle is (h,k) and the radius is r. Substitute…

Q: Find the standard form of the equation of the circle. Center ( - 3, 1) and tangent to the y-axis

A: The center of a circle is ( - 3, 1) and tangent to the y-axis.

Q: Find the polar form of 1 + sqrt(3i)

A: Find the Polar form of complex number  Given z = 1 + √3i

Q: Find the distance from the point (5,8) to the circle x2 + Y2 + 2x + 6y + 3 = 0

A:

Q: find the center and the length of a radius of each circle. x2 + y2 - 10x + 2y + 1 = 0

A: Consider the given equation x2+y2-10x+2y+1=0. Note that, for equation of circle x2+y2+2gx+2fy+c=0,…

Q: Plot the point whose rectangular coordinates are (3,1) What quadrant does the point lie in?

A: Given point is: (3,1) As both x and y coordinates are positive, the point lies in Quadrant I.

Q: Find the rectangular coordinates of the pair of points (2, 2π/3) and (4, π/6). Then find the…

A: The given polar coordinates are (r,θ)=2,2π3Since, the polar coordinates…

Q: The center of a circle has the coordinates (2-V2,3-V2). Show how there are no two points on the…

A:

Q: Find the standard form of the equation of the circle. Center (4, - 2) and tangent to the line x = 1

A: Center (4,- 2) and tangent to the line x=1we have to find equation of circle

Q: find the center and the length of a radius of each circle. x2 + y2 + 6x + 10y + 18 = 0

A: Standard equation of circle in center and radius form is x-h2+y-k2=r2 Where h,k is coordinate of…

Q: Find the coordinates of the foci

A: To find the coordinates of the foci of the given ellipse

Q: find the coordinates of the point at angle -26 degrees on a circle with a radius of 7.1

A: The coordinates of the point at on a circle = ? Where  radius. r = 7.1      angle, θ = -26

Q: Find the rectangular equation.

A: To get the rectangular equation from parametric equation, we try to eliminate the parameter.

Q: Write the rectangular equation by eliminating the parameter x=8cos(theta) y=8sin(theta)

A:

Q: Express x+y -16x+6y+1%3D0 as the equation of a circle in standard form. Identify the center and…

A: Given equation is x2+y2-16x+6y+1=0. The general equation of a circle centered at (a, b) with radius…

Q: Find the rectangular coordinates of the point P-). P(-)- P(-) x-coordinate of P 4 y-coordinate of P

A:

Q: Ay -2

A: A line is generally an object in geometry that doesn't bend i.e. it has no curve. It is a collection…

Q: Which quadrant in the rectangular coordinate system does the point (r, 0) = (5, 300°) lie in?

A: (5, 300degree)

Q: Convert r = 3sin(θ) to an equation in rectangular coordinates.

A:

Q: Show that the equation represents a circle by rewriting it in standard form. x2 + y2 − 8x + 10y +…

A: Given: x2 + y2 − 8x + 10y + 25 = 0

Q: Find the Cartesian coordinates of the given point. (- 5,0)

A:

Q: Write the corresponding rectangular equation by eliminating the parameter 0 x = 5 +3 sec 0 y = -3 +…

A: Solving the problem by eliminating the theta.

Q: find the standard form of the equation of each circle.   Center 12, 32 and tangent to the x-axis

A: we have to find the standard form of the equation of each circle with center (12, 32 )  and tangent…

Q: Question 1 What is the distance between the point (-2, 5, 3) and the z-axis?

A: The objective is to find the distance between the point (-2,5,3) and the z -axis.

Q: Find the Rectangular equation. X-5cos() and y=53in(6)

A:

Q: Find the rectangular equation

A:

Q: The equation of the circle tangent to both axes with the center in the fourth quadrant and radius 2…

A: Equation of the circle is given by: (x-h )2 +( y-k )2 = r2 Where, (h,k) is the center and r is the…

Q: could you please show the steps of how you obtained that rectangular equation? thank you!

A: As per the question we are given the equation of an ellipse in parametric form, and we have to find…

Q: Find the length of the major and minor axes and find the coordinates of the foci.

A: Given x-02625+y-52400=1

Q: Find the standard form of the equation of the circle. Center (2, 3) and tangent to the x-axis

A: The center of a circle is (2,3). The circle is tangent to the x-axis. We know that when the circle…

Q: find the center and the length of a radius of each circle. x2 + 10x + y2 + 2y - 38 = 0

A: Given the equation of a circle: x2+10x+y2+2y-38=0

Q: A soccer field is 115 yards long (x-axis) and 74 yards wide (y-axis). The field crew needs to find…

A: Given problem:- A soccer field is 115 yards long (x-axis) and 74 yards wide (y-axis). The field crew…

Q: Convert to rectangular coordinates: 1 = 2t- 1. y = t +2 for tin (-oo, o0)

A: Given: To convert into rectangular coordinates x=2t-1, y=t2+2 for t in (-∞, ∞)

Q: Find the rectangular coordinate of each point. (-2, 4)

A: Given : -2,3π4

Q: Convert the equation 5x2 + 2y? = 3z to spherical and cylindrical coordinates.

A: We have the following facts:

Q: Find the points on the circle x^2+y^2=45 that are closest to and farthest to from(1,2)

A: Given: The equation of a circle is x2+y2=45   To determine: The points on the circle x2+y2=45 that…

Q: Find the coordinates of the point on the unit circle corresponding to W(-π/3)

A: solution is given below..

Q: Given the center (−9,1)(−9,1) and the radius r=9r=9, identify the equation.

A:

Q: Give the equation of the circle centered at the origin and passing through the point (0, 8). O=0

A:

Q: Find the angle formed by the li 3x+4v-12=0 with the x-axis.

A: The slope of a line: The change in y-coordinate with respect to the change in x-coordinate of a line…

Q: 1 2 X= (y+7)¯-1 2

A:

Q: 1. Find the distance between the points A(1,2) and B(3,4) in simplest radical form.

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Given the equation, (x-h+v-k)² =r?,what are the coordanates of the center? The coordinates of the…

A: Answer and explanation is given below....

Q: If the abscissae of points A, B are the roots of the equation x² + 2ax - b² = 0 and - ordinates of…

A: The abscissae of points A, B are the roots of the equation x2+2ax-b2=0 and ordinates of A, B are…