Find the points on the circle x^2+y^2=45 that are closest to and farthest to from(1,2)

Q: The circle whose equation is ((x+3)^2)+((y+4)^2)=17 and the line whose equation is y= 4x+25 are…

A: Given query is to find the the point of tangency.

Q: Find the length of the arc of the curve 9y2 = 4x3 from the origin to the point (4,). %3D

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Q: Find an equation of the line through the point ( 3, 5 ) thatcuts off the least area from the first…

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Q: Find the point in the first quadrant where the line y=4x intersects a circle of radius 5 centered at…

A: Equation of circle : x-h2 + y-k2 = r2 ; where (h,k) is center and 'r' is the radius .

Q: Find the length of the arc of the curve 9y2 = 4x3 from the origin to the point (3,2v3).

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Q: Write the equation of the circle centered at (4, 2) with radius 18. --

A: Given, center(4,-2) radius =18 what is equation of circle

Q: Find length of arc of the curve 9y2=4x3 from the origin to the point (3, 2√3)

A: Given curve is 9y2=4x3, and the point is 3,23.   The objective is to determine the length of arc of…

Q: Show that the circle can be drawn touching line 3x+y-6 =0 at (3,3) and touching the line 3x+y+2=0 at…

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Q: Find the slope and y-intercept of the line through the point (1,5) that cuts off the least area from…

A: In the question we have to find slope of line and y-intercept.

Q: Solve the center qnd radius of the circle passing through the points P(1,1) and is tangent to the…

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Q: Next There is a line through the origin that divides the region bounded by the parabola y = 4x –…

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Q: opens upward with vertex at (-12,-6) with directrix y=- 17

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Q: Find the equation of the line tangent to a circle with center at (3,2) and radius 5 at the point…

A: The center of the circle is:  (h, k) = (3, 2) Radius of the circle is:  r = 5 Now we have to find…

Q: Find an equation of the line through the point (3,5) thatcuts off the least area from the first…

A: The line with slope m (where m < 0 through (3, 5)).

Q: Find the points where the line y=x4 intersects a circle of radius 2 centered at the origin. Give…

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Q: Find the slope and y-intercept of the line through the point (10,9) that cuts off the least area…

A: Equation of line in point slope form : (y - a) = m*(x-b)  Where, slope = m and point = (a,b)

Q: There is a line through the origin that divides the region bounded by the parabola y = 4x – the…

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Q: What is the equation of a circle with its center at (0,–2) and passing through the point (3, –5)?

A: Given,          The equation of a circle with its center at 0,-2 and passing through the…

Q: Find the area of the segment of a sphere formed by revolving the graph of     y = √(9 − x2) , 0 ≤ x…

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Q: If the point (6, -1) is reflected over line y = 2 then dilated by 2, what would the new points be?

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Q: There is a line through the origin that divides the region bounded by the parabola y = 4x – axis…

A: Solution

Q: What equation is tangent to the circle (x-4)+ (y-2)- 25 at the point (8,5)?

A: We have to find the equation of the tangent to the circle x-42+y-22=25 at the point 8,5.

Q: Find the equation of the tangent line to the ellipse 25x2+ y2 = 109 at the point (2, 3

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Q: Find the diff equation of family of circles with center on the line y = -x and through the origin.…

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Q: There is a line through the origin that divides the region bounded by the parabola v X-axis into two…

A: Given- There is a line through the origin that divides the region bounded by the parabola y = 7x -…

Q: There is a line through the origin that divides the region bounded by the parabola y = 3x – 4x² and…

A: we have been given the parabola y=3x-4x2 to find the points put 3x-4x2=0⇒x(3-4x)=0⇒x=0, 34…

Q: The tangent line to a circle may be defined as the line thatintersects the circle in a single point,…

A: The tangent line to a circle may be defined as the line thatintersects the circle in a single point,…

Q: Find the equation of the line through the point (2, 5) that cuts off the least area from the first…

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Q: There is a line through the origin that divides the region bounded by the parabola y = 4x - 5x² and…

A: Given that equation of parabola y=4x-5x2let ,equation of line y=mx   where slope=m which is devide…

Q: Find the coordinates of the point at -50° on a circle of radius 4.7 centered at the origin.

A: x=r cos θ , y=r sin θr is the radius, θ=-50°

Q: There is a line through the origin that divides the region bounded by the parabola y = 5x – 7x² and…

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Q: There is a line through the origin that divides the region bounded by the parabola y = 2x – 3x2 and…

A: According to company rule, we can answer only first question and rest can be reposted.

Q: There is a line through the origin that divides the region bounded by the parabola y = 4x – 3x and…

A:

Q: Find the points of intersection of the circle C of radius 3 centered at (-1, -2) and the line L with…

A: Want to find:                         the points of intersection of the circle C of radius 3…

Q: There is a line through the origin that divides the region bounded by the parabola y = 7x- 3x2 and…

A: Given the parabola : y=7x-3x2Let the line through the origin be : y=mx   , where m is the slope of…

Q: Give the equation of a circle tangent to the line 3x + y -2 = 0 at (-1, 5) and with a radius equal…

A: Topic = Circle

Q: There is a line through the origin that divides the region bounded by the parabola y = 7x – 2x and…

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Q: Write down the slope, of tangents of circle x +y2 =25 parallel to order 3x- 54 +8=0

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Q: 4. Center at (-4,9), tangent to the x-axis 5. Center at (-4,9), tangent to the y-axis

A: In this question we have to find the equation of the circle tangent to the x-axis and y-axis.

Q: There is a line through the origin that divides the region bounded by the parabola y = 2x – 8x and…

A: There is a line through the origin that divides the region bounded by the parabola y=2x-8x2 and the…

Q: When a figure is dilated and the segments pass through the center of dilation, the pre-image will be…

A: Here, we have given that a figure is dilated and the segments pass through the center of dilation.

Q: There is a line through the origin that divides the region bounded by the parabola y=8x−6x2 and the…

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Q: There is a line through the origin that divides the region bounded by the parabola y=7x-(2(x)^2) and…

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Q: What is the radius of a circle whose center is at (-6,7) and is tangent to the y-axis?

A: Given that: center=-6,7 and tangent to the y-axis

Q: Find the equation of one of the tangent lines to the circle x2 + y2 = 52 that pass through the point…

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Q: Find the slope and y-intercept of the line through the point (1,2) that cuts off the least area from…

A: Given : Point ( 1 , 2 )  It cuts off the least area from the first  quadrant

Q: There is a line through the origin that divides the region bounded by the parabola y = 2x-6x and the…

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Q: Find the length of the arc of the curve 9y2 = 4x³ from the origin to the point (4, ). %3D

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Q: At what point in the first quadrant does the line with equation   y = 0.5 x + 4   intersect the…

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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.