How many lines are tangent to both of the circles  x2 + y2 = 4  and  x2 + (y − 3)2 = 1?   At what points do these tangent lines touch the circles? (Enter your answers from smallest to largest x-value.)

Q: Find the equation of the circle that passes through the intersections of the circles x² + y²2 - 6x +…

A: The circle passes through the intersection of  S1=x2+y2-6x+4=0S2=x2+y2-2=0 The intersection of the…

Q: Find all points on the graph of 3x2 + 6y² + 3xy = 64 where the tangent line is horizontal. y X.…

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Q: Find the distance of the point P to the line l, where l: 3x+4y=12 P:(2,-6)

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Q: . Plot each pair of points and compute the distance between them:(a) (1, 4) and (3, 2) (b) (2, 1)…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find the point on the curve 4x

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Q: The line y = 2x + b is tangent to the graph of y = 1x at the point P = (a, 1a). Find P and determine…

A: Given: The line y=2x+b is tangent to the graph of y=x at the point Pa,a. To find P and determine b.…

Q: Find the equation of the line perpendicular to = 5 through the point (7, – 9) -

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Q: a. find the standard equation of the line parallel to 3x-5y=1 that passes through (-1,2).

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Q: how were you able to get the y values of 3, 0 and 6 by substituting the x values from equation 1…

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Q: Find the distance from the point (4, 9) to the line y = 2x.

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Q: Is the line y = −4x + 4/5 parallel to the line y = 4x + 5 ?

A: We compare y = −4x + 4/5 with y=mx+bSo, m= -4

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.