1. What are the radius and center of the circle with the equation (x- 2)2 + (y- 3)²= 25? What is the equation for OA? [P(1, 5) 4 SOLUTION A(-1, 2). -4-2 O -2 4

Q: 4. What is the equation of a circle with center (2, 4) and radius 5? F. (x – 2)2 + (y – 4)2 %3D - -…

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Q: 8. Find the equation of the circle which is tangent to the y- axis, which passes through the point…

A: To find equation of Circle which is tangent to y axis, passes through point (-1,-1) and it's centre…

Q: 3. The equation of a circle centered at (1,1) with radius 4. a) x? + y? + 2x + 2y – 2 = 0 b) x2 + y?…

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Q: 13. Find the equation of a circle with center (-4,3) and radius V12. A. (x-4)° +(y+3)' = V12 в.…

A: A circle is the locus of points in two-dimensional space which are equidistant from a fixed point.…

Q: 18 What is the equation of a circle with radius 3 and center (3,0)? A x² +y? – 6x = 0 B. x? +y? + 6x…

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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: 3x + 3y? – 12x 30y – 60 = 0 is the equation of a circle with center (h, k) and radius r for: | h =…

A: See the details solution below

Q: The center of a circle lies on the line y =6x + 2 and is tangent to the x-axis at (-2,0). What is…

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Q: What is the equation of a circle that passes through the vertex and the points of latus rectum of…

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Q: Find the standard equation of the circle whose center is at (2, 2) and that passes through the point…

A: Given: Center=(2,2) Passes through the point (5,7)

Q: 7. The radius of the circle whose equation x + 6x + y – 6y – 7 = 0 is

A: Your answer Radius =5

Q: 4 Find a. the equations of the tangents to the circle x'+y +4x-2y-24 0 at the points where the…

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Q: 9. The equation of a circle is x² + y² - 6y + 1 = 0. What are the coordinates of the center and the…

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Q: Find the equation of a circle that has its center at (6, -4) and has a radius of 3. ( x + 6) 2 + (…

A: Please refer the attached image for complete solution.

Q: 5) What is an equation of the circle whose center is (1,3) and whose radius is 2? A) (x+1)2 + (y+…

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Q: 4 Find a. the equations of the tangents to the circle x + y +4x - 2y - 24 = 0 at the points where…

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Q: 5. Determine the value(s) of k such that the circle x² + (y – 6)² = 36 and the parabola r? = 4ky…

A: we have to find the value of k. the solution is following.

Q: 1. As you may already know, the general equation of a circle is: (x h)² + (y- k)² = r2, where (h, k)…

A: 1. The general equation of a circle : x-h2+y-k2=r2    (h,k) is the centre of the circle and r is the…

Q: What is the equation of the circle whose center is at (0,0) and which passes through the point…

A: Let A(x1,y1) and B(x2,y2) be the coordinates of eand points of line segment AB.Then, Length of AB =…

Q: 3 The circle with equation (x - k)² + y² = 41 passes through the point (3, 4). Find the two possible…

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Q: 12. A circle in the xy-plane has equation (x + 3)² + (y - 1) = 25. Which of the following points…

A: According to the problem, we have

Q: 3x +3y- 24x 30y + 96 = 0 is the equation of a circle with center (h, k) | and radius r for: h = and…

A: Given equation 3x2+3y2-24x-30y+96=0 The objective is to find the center and radius of a circle.

Q: 3x² + 3y² 6x6y + 3 = 0 is the equation of a circle with center (h, k) and radius r for: h = and k =…

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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…

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Q: 2x + 2y? + 20x + 4y + 20 = 0 is the equation of a circle with center (h, k) and radius r for: h and…

A: Given :  2x² + 2y² + 20x + 4y + 20 = 0 To find: center (h,k) and radius r?

Q: 18. The equation of a circle with center on the y-axis and passing through the origin and the point…

A: It is given that the circle is passing through the origin (0,0) and the point (2,3). As the general…

Q: 3a? + 3y? – 30æ – 18y – 6 = 0 is the equation of a circle with center (h, k) and radius r for: %3D…

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Q: 4. An equation of a circle written in the form x + y + Ax + By + C = 0 is called the equation of a…

A: Given, An equation of a circle written in the form x2+y2+Ax+By+C=0 is called the _________ form of…

Q: What is the standard circle equation from the general circle equation: x2 +y? +8x=144+12y O K+42…

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Q: 22. Find the center and radius of the circle whose equation is x2 – 24x + 48 = -y² + 10y О С(12, 5),…

A: The solution is given as

Q: 2. Does the equation x² + y² + z²-3x - y + 3z = 0 represent a sphere? If so, find the center and the…

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Q: 2² + y? 14x + 10y + 10 = 0 is the equation of a circle with center (h, k) and radius r for:

A: Given : x2+y2-14x+10y+10 = 0

Q: Find the equation of the circle with center 2+31 and radius4 units. (A) (x-2) +(y-3) =4 (C) (x-2)…

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Q: 3a? + 3y? – 18z – 24y + 48 = 0 is the equation of a circle with center (h, k) and radius r for: h…

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Q: x ds, where C is the portion of the parabola from (0,0) to (1, 1), followed by the line segment from…

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Q: 1. What are the center and radivs of the circle with an equatlon x2 +y? + 8x- 4y-5 = 0 2. What are…

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Q: 1. Find the equation of the center and radius of the circle: x² + y² + 4x - 8y- 5 = 0

A: Follow the procedure given below.

Q: 3x² + 3y² - 6x − 24y + 24 equation of a circle with center (h, k) and radius r for: h = and k = and…

A: We have to find the center and radius of given circle.   According to our guidelines we can solve…

Q: the standard form of the equation of the circle with center at C (0,0) and radius 5 is

A: Standard form of equation of circle (x-h)2+(y-k)2= (R)2 where, (h,k) is center of circle R = radius…

Q: The general equation of the circle that passes through the points (-3,4), (2,–6), and (5,0) is x2 +…

A: Given: Let us consider the given general equation of the circle, x2+y2+Dx+Ey+F=0 and the circle…

Q: 14. Find the radius and center of a circle with the equation x2 + y2 + 4x – 8y = 16.

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: 10. The radius of the circle with equation x² +y² – 10x + 12y + 41 = 0 is A 5V2 B 3V5 с 25 D 4V5

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Q: The equation of a circle can be represented as in-h)² + (y – k)² = r², where (h. k)ie center of the…

A: Substitute h,k and r in the equation, x-h2+(y-k)2=r2 and solve for y to yield the result.

Q: What is an equation of the circle whose center is (0,4) and whose radius is 3? A) x2+ (y- 4)2 = 9 B)…

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Q: The equation of a circle in the zy-plane is 2 + 4x + y? – 10y = 20. If the line z= k intersects the…

A: Consider the equation of circle in xy-plane given by x2+4x+y2-10y=20 If the line x=k intersect the…

Q: A circle with radius 4 has its centre at the point (2,4). The equation of the circle is 23. A (x –…

A: circle equation

Q: 1. Find the point on the parabola y = 3 – x² that is closest to the point (6, 0).

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Q: 4 Find a. the equations of the tangents to the circle x +y +4x-2y – 24 = 0 at the points where the…

A: Given,  (a) Equation of the circle   x2+y2+4x-2y-24 = 0  We have to find the equations of tangents…

Q: 33) Find the points of intersection between the line x - y - 2 = 0 and the parabola y = 4 - x 2.

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Q: 2. Find the equation (in general form) of the tangent lines to the circle x² + y² - 8x + 10y = 128…

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.