34. The graph of x² + y² – 2x – 4y - 4 = 0 is circle centered at (A) (-1, -2) (B) (-1, 2) (C) (1, -2) (D) (1, 2) (E) (2, 1)

Q: 3. Using the traces obtained in IV.1., provide a hand-drawn sketch of 3. Label all important points…

A:

Q: 21 7. The centre of symmetry of the curve y = ² - 4 1z ±2 is A (0,2) в (20) с (0,0)

A: Given that: y=2xx2-4

Q: 4. At the point (0, 0) the graph of y 4.x2 has greater curvature than does y 2x2.

A: These equation represents parabola,then Radius of curvature: K=  y'' /([1+(y')²]^3/2)

Q: 7. Find a single initial vahue problem that admits the family of solutions y = e and then find an…

A:

Q: 7-The tangent of the curve x^2+y^2- 2xy3D0 at the point (1,1), is * O a. y=2-x. O b. y=x-2. C.…

A: We find equation of tangent to the curve

Q: Find the maximum and minimum values of the function ƒ(x, y) = 3x + 4y on the circle x2 + y2 = 1.

A:

Q: 8. Show that the one parameter family of curves y² = 4k(k + x) (k E R) are self orthog- onal.

A:

Q: 5. Use traces to sketch and identify the surface x2- y? - z2 = 4.

A:

Q: Sketch the graph of the cylinder x (y – 2)² in R³. %3D

A: Solution:   First of all x-y projection of this 3d graph is

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: Consider the accompanying graphs of y = 2x + 3 and y = In x. Determine the %3D a. minimum vertical…

A: (a) Given information:

Q: Lqsudnhlao203=9m] -03P99E90RO[9U3RM7210 Ud8y(l,om8 301 29u 3 ***#!12r Families of Curves: Parabolas…

A: Topic:-  geometry

Q: 2. Evaluate dy, where C is the part of the parabola y = x² from (1, 1) to (2, 4).

A:

Q: . Consider the accompanying graphs of y = 2r + 3 and y = In x. Determine the a. minimum vertical…

A: Given, y=2x+3 and y=lnx. And, the graph is shown below: a. Let Ax,y=x1,2x1+3 and Bx,y=x1,lnx1 be…

Q: The graph, when the curve y=v(3+ x^2 ) from x = 0 to x = 4 is rotated about x - axis is ....

A: This question can be solved using the concept of volume of solid generated when curve is rotated…

Q: 9. Find the point of intersection of the two curves, * y = 2r-1 y = x-2r O(-) none of these

A: To find out the point of intersection of curves.

Q: 6. Let C C R? be the positively-oriented boundary of the graph of the circle x2 + y? = 1. Using…

A:

Q: 9. Find the point (x, y) on the line y = 2x + 3 such that the distance from (x, y) to (1, 1) is as…

A:

Q: A 2.25 m -4 m- -e=90° µ=0.1 -3 m 3 m k= 200 N /m- 3 m -2 m-F1 m- 3 m -Inx -3 m- -3 m- F(x). boundary…

A:

Q: 3. Find the line normal to the ellipse at X=-1 y= 2+4x-x3

A: Given, y=2+4x-x3 At x= -1 y=2+4-1--13y=2-4+1y=-1 Now point -1,-1

Q: If a bug walks on the sphere x^2 + y^2 + z^2 − 4x + 4y + 4z + 3 = 0 how close and how far can it get…

A:

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: b) If we are at the point (1, 2, 4) on the surface z = xy², and we move a short distance in the…

A: Please check step 2 for solution.!

Q: What are the control points of the splines Bezier curve from the two equations given below: a(x) =…

A: Given, ax=1+5x2+2x3...1bx=1-x+x3...2 The control points are lie on both the curves. So, to get…

Q: (6) Find the points on the curve 5x2 + 6xy + 5y² = 9 which are nearest to and farthest from the…

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

A:

Q: 1 Find the points of discontinuity of y = where и +и - 2 1 u = * - 1

A:

Q: 16. The y-intercept of the graph of y =asin 0 +d is Oa+d Od O-d Oa-d

A: This question is related to graph and equations, we will use basic graphical principles to solve it.

Q: The Gateway Arch in St. Louis was designed by Eero Saarinen and was constructed using the equation…

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: Prove that the curves y2 = 4x and y2-6x+1 = 0 touch each other at the point (1,2)

A:

Q: Prove that the curves y2 = 4x and x2+ y2-6x+1 = 0 touch each other at the point (1,2)

A:

Q: 7.Find the maximum and minimum distances from (0,0) to the curve 5x2+6xy+5y2=8

A:

Q: 1. Find the shortest distance from the point (1,0, –2) to the plane x+2y+z = 4.

A: We have to find shortest distance

Q: Explain why a cubic Bézier curve is completely determined by x(0), x (0), х(1), and x'(1).

A:

Q: 3/2 The length of the curve x= 4y2 from y=1 to y= 4 is given by

A:

Q: Find the total length of the loop of the curve 6y^2 = x (x - 2)^2 between x = 0 and x = 2.

A:

Q: 5 Find the valume of the Sotids abtaind by-revelving the Yegion in the firstquadrand boundby the…

A: Sketch the graph and find the region. Using shell method, volume is evaluated.

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: 9- Suppose T degrees is the temperature at any point on the sphere x² + y² + z² = 4 and T = 50x²yz.…

A: The temperature is

Q: 1. Sketch the graph of the level curves of the surface z = y + x^2 when k = −2, k = 0, and k = 2

A: Level curves problem.....

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 minimum distance from the point (1, 1, 11) to the paraboloid given by the equation z = x² +…

A:

Q: 27. The equation of the common tangent to the circles x+ y - 12x- 2y-123D0 and x*+y - 4x + 4y + 4 0…

A: Note: "Since you have asked multiple questions, we will solve the first question asked by you. If…

Q: -8x If the infinite curve y = e8x, x 2 0, is rotated about the x-axis, find the area of the…

A: Given curve is y=e-8x, x≥0 is rotated about x axis.

Q: 5. The coordinates of the vertex of the curve y = 1- 2x - 4x² are: A. G ) B. (- 5 ) €(- ) D.(- -) 1…

A: Hi, for question 6 repost

Q: Find the point on the curve of intersection of the paraboloid x – y + 2z = 0 that is dosest to the…

A: Here we have to find the point of intersection of the paraboloid x2+y2+2z=4 and the plane x - y + 2z…

Q: 1 Find the points have minimum distance From the origih to the Surface xyz =1.

A: Using the lagrangian ultiplies Let For critical points,

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.