Find the point on the line x + 2y = 5 that is closest to the origin.

Q: The point on the curve y = 2-x nearest to (3,2) is (1,1) (0,2)

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Q: Find the abscissa of the point on the graph of y=V 2x – 1 that is parallel to the line 2x - y+1=0

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Q: 4. Find the equation for the line tangent to a. y=x²- 3 x + 5 at the point (2, 3)

A: We will find tangent equation.

Q: Find the point (x0, y0) on the line 4x + 9y = 12 that is closest tothe origin.

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Q: b. Enclosed by the curves y² = 4x + 4 and the line y = 4x – 16.

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Q: 15. Find the point on the line y 3x that is closest to the point (50,0).

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Q: Find the equation of a line normal to the graph of y = 3x+5/x−1 at x = 3

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Q: Find the length of the curve y = x2, 0 ≤ x≤√3/2.

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Q: Find the points on the curve x^2y = 2 nearest the origin.

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Q: Find the slope of the line normal to the curve y = x³ - 2x +1 at x = 2 -

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Q: Find the point where the line tangent to y=x* – 3x² +2 at (2, 6) crosses the x – axis.

A: y=x4-3x2+2,  2, 6 Differentiating with respect to x, we get dydx=4x3-32x+0=4x3-6x Now slope of the…

Q: Find the exact length of the curve. y=3+8x3/2, 0 less than or equal to X less than or equal to 1.

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Q: Find the equation of the line segment tangent to the curve y−2x2−1=0y−2x2−1=0 which is parallel to…

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Q: The x coordinate of the point of intersection between the two curves Y = e2lx and y = 1 is

A:

Q: Find the slope of the curve 1 at the point P (2, ;).

A: Explanation of the answer is as follows

Q: Find the point on the graph of y = 3x2 − 2x + 5 where the tangent line is perpendicular to the line…

A:

Q: Find the equation of the line segment tangent to the curve y−2x^2−1=0 which is parallel to the line…

A: Given curve is y-2x2-1 = 0

Q: Find the point on the curve y =√ x that is closest to thepoint (3 ,0) .

A: Let (x,y) be the point on the given curve which is closest to the point(3,0) where The distance…

Q: Find the point on the Curve y rx that is closest to the point (2,0)

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Q: Find the point on the curve y = /2x + 3 which is closest to the point (5, 0).

A:

Q: Find the point(s) of intersection of the parabola y =x2+ 2 andthe line y = x + 4.

A: The given functions are y=x2+2   and   y=x+4

Q: Find the slope of the curve at the given point: y = x(4x − 1)², (1, ²) -

A: Given query is to find the slope of the curve at given point.

Q: Find the equation of the line tangent to 3x²y + 4xy2 = 6x² + 5y at the point (1,).

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Q: Find the equation of the line tangent to y = x2 - 1 going through x = 1

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Q: Find the point on the x-axis that is equidistant from the points (0,−1) and (5,−3)

A: To find the coordinates of the point satisfying the given conditions

Q: 4. Find the equation for the line tangent to a. y= x²- 3 x + 5 at the point (2, 3)

A:

Q: Find the slope of the curve x^2 + y^2 - 6x + 10y + 5 = 0 at point (1,0) * O 1/5 O 2/5 O 1/4 2 O O O…

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Q: Find the length of the curve y = x3/2 from x = 0 to x = 3.

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Q: Find the closest point to the point (2,0) on the y = x curve.

A: To find the closest point to the point (2,0) on curve y=x

Q: Find the length of the curve x = y2 — 2y, 0 ≤ y ≤ 2.

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Q: Find the length of the curve y=7x-13 between y=-6 and y=15.

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Q: ) Find the slope of the curve x +y3- 6x²y = 0 at x = 1

A: Slope of a curve: For non- linear functions, the rate of change varies along the given curve. So,…

Q: Find the length of the curve y x7 from ¤ = 0 to x = 15. 2/3

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Q: Find the point on the curve y = √x closest to the point (2,2)

A: Here we have to find the point on the curve y = sqrt (x) closest to the point (2, 2)   use the…

Q: find the equation of the secant lines of y=√x passing through the points: x1=1 and x2=2

A: Secant line for a function between two points on a curve is simply a straight line passing through…

Q: At what points will the line y=x intersect the unit circle x2  + y2 =1?

A:

Q: Find the slope of * y+ Vx+ y =x at (3,1)

A: A detailed solution is given below

Q: Find the points on the line 2x+y=5that is the closest to the origin.

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Q: Find the point on the line y 2 x-3 that is nearest to tne ofigin.

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Q: Find the slope of the line normal to the curve y x3 – 2x + 1 at x = 2

A: Our Aim is to find the slope of the line normal to the curve y=x3-2x+1-(i) at x=2.

Q: / Find the length of the curve y = (÷) (x²

A: Given,         y=13x2+232

Q: Find the equation of the line normal to x^3 + y^3 = 6xy at (3,3)

A: Given, x3+y3=6xy

Q: 9. What point on the line y=3x+4 is closest to the origin?

A: Given that: y=3x+4

Q: B. Find the point on the line y = 10 – 2x that is closest to the origin. REFLECTION

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Q: Find the point (Xo, Yo) on the line 4x + 6y = 12 that is closest to the origin. (Xo, Yo) =

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Q: Find the equation of the family of curve whose slope at any point (x,y) is 3x^2+4

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Q: The x coordinate of the point of intersection between the two curves 12x y = = el2# and y = 1 is x =

A: Our Aim is to find the x coordinate of the points of intersectionbetween the two curves y=e12x and…

Q: Find the slope of the curve x3y3 + y2 = x + y at the points (1, 1) and (1, -1).

A: Given,

Q: Evaluate the length of the curve y = 3 + 3Vx +1 , 0<x< 3

A:

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.