Find all points on the y-axis that are 6 units from the point (4, - 3).

Q: Plot the points from the table onto the coordinate plane below. y -5 3 -3 -4 -4 -1

A:

Q: Solve for y and write an equation for a line perpendicular to y=−5x−3 and passing through the point…

A: The line perpendicular to the line y=-5x-3 and passing through the point 15,4

Q: Find the distance between the points a 1 - 2 (−1) and b Distance = -4 -4 3

A: This question can be solved using the concept of distance formula.

Q: Find the intersection point of the line 3x-2y 0 and the line passing through the point (-1,0) and…

A:

Q: Perpendicular with y= -1/2x and passes through (2,5)

A:

Q: Plot two points that are both 3 units away from the x-axis and 3 units away from (5, 4). (Hint: Use…

A:

Q: Find an equation for the set of points equidistant from the x-axis and the y-axis.

A: Let the point be (x,y,z) which is equidistant from the x-axis and the y-axis. Concept used:

Q: The point that is 2 units to the left of the y-axis and 4 units above the x-axis has coordinates (,.

A: A point which is a units to the left of y-axis and b units above the x-axis is given by the…

Q: Find all points having an x-coordinate of 3 whose distance from the point (- 1, - 4) is 5. The…

A: Given point is  (-1,-4). and distance is 5.

Q: x2-5х-6 y = (х+3) (х-3)

A: y=x2-5x-6x+3x-3 We have to find the values of x at which the given y is discontinuous.

Q: Find the equation of the line parallel to 6x + 2y = 7 passing through the point (5, 4). y =

A:

Q: Find the point on the line  y = 4x + 3  that is closest to the origin

A:

Q: Find the coordinates of the point on x axis which is equidistant from (-2,5) and (2,-3)

A:

Q: Which points on the graph y = x² are closest to the point (0, 4)?

A: Since multiple questions are asked , According to guidelines I will answer the first one.

Q: Find an equation for the set of points equidistant from the point (0, 0, 2) and the x-axis.

A: To determine the equation for the set of the points.

Q: Which points on the graph of y= 4-x^2 are closest to the point (0,2)?

A: Given function- y=4-x2 Any point on the curve of this function will be given by- x,4-x2 The given…

Q: Find the distance, d=(za - z)² + (y½ - y) between the two points. Round to the nearest tenth. %3D C…

A: Designating the point as (x1,y1) and (x2, y2) is arbitrary we choose (x1,y1) = (2,4) ( x2,y2) =…

Q: Find the point on the y-axis which equidistant from the point A (6,5) and B (-4,3)

A: Please refer to the image below

Q: about the y-axis

A:

Q: Find the equation of the line passing through the point (3, 1) and perpendicular to –31+y= 12.

A:

Q: points

A: Please refer to the image below

Q: Determine the slope 3(x2+y2)2=100xy at the point (3,1)

A:

Q: Find the area of the triangle that lies in the first quadrant (with its base on the x-axis) and that…

A: y=2x-4 and y=-4x+20 We need to find the area of the triangle that lies in the first quadrant (with…

Q: Find an equation for the contour of f(x, y) = 2a²y + 6x + 15 that goes through the point (4, 1).…

A: A contour line of the quadric surface is the curve of intersection of the quadric surface with the…

Q: Find the point on the line −5x+2y+6=0 which is closest to the point (0,−1). Answer =

A:

Q: Find the distance from the point (1,3) and the line 3x+4y+53D0

A:

Q: Find all points on the x-axis that are 6 units from the point .(4,-3)

A: Consider the point on the x-axis be (x, 0)

Q: at the point P(x, y) = (-4.5, –16.73), determine the values of 0, and 0,.

A: In the given diagram below,   We have to determine θ1  and θ2 . In ∆OPB   Using Pythagoras…

Q: find x and y intercept for y=square rood of 2x-1

A: given: y=2x-1

Q: Find the image of the point (1,2) in the straight line 3x+4y-1=0

A:

Q: Graphically, find the point (x1, y1) which lies on both lines 2x + y = 4 and x −y = 2.

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Q: Find the equation of the line perpendicular to 3x + 5y = 3 passing through the point (5, 2). y =

A:

Q: Find the point on the x-axis that is equidistant from the points (1, 2) and (2, 3). The coordinates…

A: soln:point on x-axis which is equidistant from the points 1,2 and 2,3

Q: Find the point when the line y=-3x+8 that is closest to the origin.

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Q: Find the point on the line y = 2x that is closest to the point (5, 2).

A:

Q: Find the point on X-axis which is equidistant from (2,-5) and (-

A:

Q: Find an equation for the contour of f(x, y) = 2x2y + 6x + 10 that goes through the point (2, -2).

A: We have to find an equation that is the contour of  f(x,y)=2x2y+6x+10      that goes through the…

Q: Find an equation of a line parallel to y-3x=5 and passing through the point (2,2) y=?

A: parallel to y= 3x + 5  p(2,2)

Q: y = 6x?, 1, and y 0, about the -axis.

A:

Q: The y coordinate of (-2, 4) is what?

A: Given, -2,4 To find the y - coordinate of the point.

Q: Find the point on the line y = 5x + 4 that is closest to the origin. (х, у) %3

A:

Q: Find the point on the line 3x-4y-1=0 which are at a distance of 5 units from the point (3,2)

A: To Find: The point on the line 3x-4y-1=0 which are at a distance of 5 units from 3,2. Concept:…

Q: Find the equation of a line perpendicular to y=−4x that contains the point (−3,−4).

A: If a line is perpendicular to another line, then the product of the slopes of the two lines is…

Q: Find the point of the line y = 2x − 1 that is closest to the origin.

A:

Q: Find the point on the y-axis that is equidistant from the points A(-4,-2) and B(3,1).

A: Given points (-4,-2) & (3,1)Point on y-axis means x-coordinate is zero i.e.,point is (0,y)

Q: Find all points on the x-axis that are 14 units from the point (6, - 7).

A:

Q: Which of the following is the y-coordinate for the point that lies on the line y=-3/4x+1 and has an…

A: substitute the  value of x .

Q: Find all points on the x-axis that are 5 units from the point (4, - 3).

A: Solution Given (x1,y1)= (4 -3) y2 = 0          (point lies on x- axis) we know the distance formula…

Q: reflect the point (2, -4) over the y-axis

A: If we reflect a point over the y-axis then the formula is: (x, y)→(-x, y) Here x=2 and y=-4

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.