12. A circle in the xy-plane has equation (x + 3)² + (y - 1) = 25. Which of the following points does NOT lie in the interior of the circle?

Q: Write the standard from of the equation of the circle with center at (-3, 5) that is tangent to the…

A:

Q: 5. Prove that whole length of the curve x3 + y2/3 = a/3 is 6a.

A: Given that x23+y23=a23 To find the length of the curve:…

Q: 3/2 Find the length of the curve. y = (x* +4)" OSxs2

A: see below the answer and calculation

Q: For what values of a and b is the line 5x + y = b tangent to the parabola y = ax? when x = 4?

A: y=ax2y'=2axy'(4)=2a(4)y'(4)=8a Now we have 5x+y=b ⇒y=-5x+b Compare with the equation y=mx+b From…

Q: .2 Use Green's Theorem to evaluate x-ydx - xy² dy , where C is the circle x +y² = 9 with…

A:

Q: 1. Using Euler's equation, show that the shortest distance between two points (r1, yn, z1) and (r2,…

A: Given, the points are (x1, y1, z1)   and  (x2, y2, z2).

Q: 13) Find the points of intersecti on of the parabola and the line. y=2x^2-3x-1 and y=x+5

A: Equate the equations with each other and solve for x to find the point of intersection .

Q: 1. Given to the right is the graph of a portion of four curves: x = 0, y = 1, x – V3y = 0 and a? +…

A: Given: slope of line,m values.... Let us solve step by step

Q: Suppose surface #1 is defined by o =45° , 0 <ps9, 0 < z< 6 and surface #2 is defined by 0 =56.3° The…

A: given:

Q: 5. Tangent B. Determine the center and radius of each circle: 6. x2 + y2 =16 7. (x-2 )2+ y2 - 13 8.…

A:

Q: 1) The maximum distance from the origin of the xy plane to the circle described by (x – 12)? + (y –…

A: given equation of circlex-122+y-62=16 As per our guideline we supposed to answer only first question…

Q: 4 and Consider the region in the second and third quadrants between the circles x² + y² = x² + y² =…

A: Concept: cartesian coordinates can be converted into polar coordinates using trigonometric functions…

Q: Find the center of the circle tangent to x^2 + y^2 + 2x - 6y + 5 = 0 at (1,2) passing through point…

A:

Q: A surface in R³ is defined by the equation 4z = x² + 4y“.

A:

Q: 5. Consider the two curves y = x° - 3x + 20x + 88x² + 71x – 74 and y = 2a+ 50x – 22x + 42.x + 31. |…

A:

Q: Prove that the curves x2−y2=3 and xy=2 intersect at the right angle.

A:

Q: 8., (x + y) dA, where R is the region that lies to the left of the y-axis between the circles x? +…

A: As you have asked to answer question 8, we will answer question 8.Question 8.The given integral…

Q: Evaluate |2*(x +7) – 2y ds C where C is the circle of radius 1 centered at (-3,0) and lying on the…

A: Since the integral ins on the plane x=-3 so the integral becomes:  ∫Cz3x+7-2yds=∫Cz3-3+7-2yds…

Q: 1- What is the value of f 3z2+7z+1 dz z+1 (a) If C is the circle |z+1|=1. (b)If C is the circle…

A:

Q: A surface in R³ is defined by the equation 4z = x² + 4y².

A: Given:-                 The surface in  is given by  . Sketch the intersections (traces) of this…

Q: 16 6xy ds, where C is the right half of the circle x² + y² = 4. Evaluate the line integral

A:

Q: What is the shortest distance from the surface xy +12x +z^2 =144 to the origin?

A: To find the shortest distance from surface xy +12x +z2 =144  to origin.

Q: The family of curves orthogonal to x2 + 4y2 = c2 has the general equation 04. %3D

A:

Q: 15. When a line L is tangent to the circle 2 + v = 100 at the point (a, 6), find the equation of…

A:

Q: 4. Find the exact length of the curve. 36y2=(x²-4)3,2≤x≤3.y≥1

A:

Q: (2) Find the Ualue of the constant m while the Curl of Foaoy,z) = (mxy- 2) Ĉ +cm-2)x)+(1-m)x2° Â is…

A: Please see the answer in step 2

Q: 6. Prove (by plot) the equation (x²+y²=16) is the circle in 2D , and cylindrical in 3D.

A: We will answer the first question since we don't answer multiple questions at a time. Please…

Q: Evaluate O (6y+x)dx+(y+2x)dy where C is the circle (x-2)²+(y-3)² = 4 Without using Green's Theorem.

A: We will find out the required value.

Q: The tangent to the circle x2 +y2 +10 x+5 y= 60 at the point (2 ,4) is Select one: O None O 13 y +…

A: Given that:x2+y2+10x+5y=60

Q: 4. Let C be the the circle ² + y² = 4 and Calculate the work(W = [,F dr when C is traversed in the…

A:

Q: 4. Evaluate / (z – 2) dz where C is the lower half of the circle |2 – 2| = 4.

A: Note: According to bartleby guidelines we have to answer only first question please upload the…

Q: Evaluate |*(x + 7) – 2y ds where C is the circle of radius 1 centered at (-3,0) and lying on the…

A:

Q: Find the length of the tangent to the circle x² + y² − 2x − 3y − 1 = 0 from the point (2, 5)

A: Solution- The equation of the circle x2+y2-2x-3y-1=0 The point =2,5 length of the tangent

Q: Determine the shortest distance from the surface xy+3x+z2=12 to the origin.

A: Given surface equation is

Q: Evaluate f. y3 dx - x3 dy where c is the circle x2 + y2 = 4

A:

Q: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is a)…

A:

Q: 4) Suppose that the level curves of a function z = f (x, y) consists of straight lines. Must the…

A: Given that level curve of a function z=f(x,y) consists of straight lines.

Q: What is the shortest distance from the surface xy + 6x + z² = 48 to the origin? distance =|

A:

Q: 6. Compute G.T ds if K is the portion of the circle x2 + y* = 7 in the third quadrant (oriented…

A: region of integration is part of circle, x2+y2=7, lying in 3rd quadrant, thus, limits of x,y are -7…

Q: 6.2 Finl the Voune of the Selid enclosed by the curves y=eX, y=0 x=0,'= "about the x-axs.

A: Given: y=ex, y=0, x=0, x=1 From the given curves the bounded region is as shown below; Apply the…

Q: What is the shortest distance from the surface xy+3x+z^2=12 to the origin?

A: Let (x ,y, z) any point on surface. We have to minimize function f(x,y,z) = x2 + y2 + z2 under…

Q: Consider the equation хд,и — удуи — -и with the initial condition: u(x,y) : = 2 on the circle {(x,y)…

A: Given the equation as x∂xu-y∂yu=-u                  (1) write down the subsidiary equation of (1)…

Q: What is the equation of the circle concentric with circle(x-2)2 + (y+1)2 = 5 that is tangent to the…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: 6. Find the area and centroidal distances of the curve that lies between the equations y-4-x^2 and…

A:

Q: Find the exact length of the curve. 36y² = (x²-4)³, 4≤x≤6, y 20

A:

Q: b) Find the points on the curve 2 17x + 12xy + 8y“ = 100| that are farthest away from the origin…

A: Substitute x = rcosθ and y= rsinθ

Q: Find the length of the curve ƒ1x2= x3&gt;2 between x = 0 and x = 4 (as shown).

A: Given curve is fx=x32. To find the length of curve between x=0 and x=4. Solution: We know that…

Q: Q2 Calculate 8- Z -dz, (4 – 2) where C is the circle of radius 7, centre 0, negatively oriented.

A:

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.