5. Determine the value(s) of k such that the circle x² + (y – 6)² = 36 and the parabola r? = 4ky will intersect only at the origin.

Q: 7. Find the exact length of the curve: y = 1 + 6x³/², 0 < x < 1.

A: The length of the curve is calculated from the graph.

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

A:

Q: Find the length of the arc of the parabola x2 = 4y from x = -2 to x = 2. А. 4.3 В. 4.6 С. 4.9 D. 5.2

A: we have to find the length of the arc of the parabola x2=4y from x=-2 to x=2

Q: 1. Find the center and radius of a circle given by 2r2-8x + 2y2-4y+6=0

A: Given: 2x2-8x+2y2-4y+6=0 Take out common and write in standard form x2+y2-4x-2y+3=0

Q: 2. Consider any five points P1, Ps in the interior of a square S of side length 1. Show that one can…

A: To solve this problem we use the Pigeonhole principle . Pigeonhole principle : If there are m holes…

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

A:

Q: 2. Consider any five points P1, Ps in the interior of a square S of side length ... 1. Show that one…

A: Since you have asked multiple questions here, we will solve the first question for you. To get the…

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: Find the distance between the point (p, 4p) and the parabola y? = 2px, where p is a fixed positive…

A: let the point on parabola be A= (x, y)  B = (p, 4p) Thus,  AB = x-p2+y-4p2 but parabola is y2=2px…

Q: 1. Transform the general equation of the circle x² + y² + 8x - 2y - 8 =0 into its standard form and…

A:

Q: Find the area of the resulting surface if an arc of a parabola y = x² from (1,1) to (2,4) is rotated…

A: Given

Q: A] Find the length of the arc of the semi-cubical parabola y2 x (1,1) and (5,5V5). 8250 between the…

A: Solution:Given        y2=x3    between the points (1,1) and (5,55)To find the Arc…

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

A:

Q: Find the center and radius of each circle. 1. x2+y2 25 2. (x- 1)2+ (y+ 1)2 = 49 3. (x+ 2)2 + y2 = 36…

A: The general equation of a circle is (x-h)2+(y-k)2=r2,  Where h= x-coordinate of the center of circle…

Q: Show the complete solutions. Family of circles centered at the line y = 2x. Ans: y" (y-2x) + 2(y')³…

A: To find out the differential equation for the family of circles having centre on the line y=2x.

Q: Demonstrate that the circles (x- 2)² + y² = 2 and x? + (y – 2)? = 2 share tangent at point (1,1),…

A:

Q: For what minimum integer value of a, will the line ax+(a+1) y =18 www (a> 0) have two intersection…

A: If the line cuts the circle at two points then given line is secant line of the circle .The…

Q: If the infinite curve y = e-6x, x > 0, is rotated about the x-axis, find the area of the resulting…

A:

Q: Show the complete solutions. Family of circles centered at the line y = 2x. Ans: y" (y-2x) + 2(y')³…

A: Given problem:- Differential equation of family of circles centerd at the line y=2x

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

A:

Q: 1. Find the standard form of the equation of the circle tangent to both axes at (-3,0) and (0,3).

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: If PP' is a diameter of the rectangular hyperbola xy = c' show that the locus of the intersection of…

A: given , if PP' IS a diameter of the rectangle hyperbola xy = c^2  show that the locus of the…

Q: Determine the value(s) of k such that the circle x²+(y-6)²=36 and the parabola x²=4ky will intersect…

A: Consider the provided equations, x2+y-62=36  ....... (1) x2=4ky ...... (2) Determine the value(s) of…

Q: (1) Find a point P in the first quadrant on the curve f(x) = such that the rectangle with sides on…

A: In the question we have to find the perimeter of the rectangle.

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: Exercise 1.2.16 Find the circle x2 +y² +ax+by+c=0 passing through the following points.

A:

Q: 4. Find the two values of a for which the line connecting the point (1, –1) to a point (a, a²) on…

A:

Q: 15. Complete the squares on x- and y-terms of the circle: 4x + 24x + 4y + 36y =0. SLO 12

A:

Q: If a parabola defined by f(x)=2−x^2 is inscribed under an equilateral triangle ABC, so that the…

A: Given data:     The given equation of parabola is: f(x)=2-x2.     The below figure represents the…

Q: 1 Write the general equation of cach of the following circles that satisfies the stated conditions.…

A: In the question it is asked to calculate the equation of circle for the given question.

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: Consider the circle with two intersecting chords. D x+2 x-1 x+5 Solve for x. 1.

A:

Q: If the radius of the circle x2+y2-8x+10y+k=0 is 9. Then find the value of K

A:

Q: The graph of x + z² = 1 is an ordinary right circular cylinder. Indicate axis of the cylinder lies…

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Q: in R°sketch the graph of the cylinder x = (y – 2)?

A:

Q: - Show that the distance r from the origin O to the point P(Coshu,Sinhu) - on the hyperbola x-y 1 is…

A:

Q: Consider the region in the fourth quadrant between the circles x² + y² = 4 and x² + y² = 25 and…

A: answer is in next step. please give a like !!

Q: 6. Show that if m is any real number, then there are exactly two lines of slope m that are tangent…

A:

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

A: Given x2+y2-2x-4y-4 = 0  ....(1)(1) is circleNow compare standard equation of  circle is…

Q: Suppose Vf(x, y) = 3y sin(xy)i + 3x sin(ry)j, F = Vf(x,y), and C is the segment of the parabola y =…

A:

Q: 8. centered at Which of the following equations represents the circle with radius F 16x2 + 16y2- 16x…

A:

Q: Which graph is the one described by the set of parametric equa Sz = t ly = t³ %3D for -0<t < o∞ ?…

A: Given:  x = t , y = t3