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

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 an equation for the contour of f(x, y) = 2x°y+ 8x + 15 that goes through the point (5, 2).

A:

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: Which points on the graph of y = 4 - x2 are closest to the point (0,2)? Ans. and

A: We will use Lagranges multiplier to find nearest points on graph

Q: Find the equation of the line passing through the point (2, 3) and parallel to the x-axis.

A: Given that the line is parallel to x-axis it implies the slope of the line will be equal to zero.…

Q: Find an equation of the set of all points equidistant from the points A(-1, 5, 4) and B(6, 2, –1).

A: Given : A(-1,5,4) and B(6,2,-1) Let P(x,y,x) be at equidistance from A  and B Now find the distance…

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: Explain how to plot (r, θ,) if r > 0 and θ > 0.

A:

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: Find the point on the line y = 2x + 8 that is closest to the origin.

A:

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

A:

Q: List the quadrant or quadrants satisfying the condition : x3 > 0 and y3 < 0

A: The given condition is x3>0 and y3<0.

Q: Find all points having a y-coordinate of - 3 whose distance from the point   (1, 2) is 13.

A: Consider the points are A = (x,-3) and B=(1,2) The distance between A and B is 13 units.   If the…

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: s reflected in the x-axis, then the

A:

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 point on the line 2x + 6y + 5 = 0 which is closest to the point (-4, -4). (

A:

Q: Find the point on the line 6x + 2y –1 = 0 which is closest to the point (-7, –7).

A:

Q: Suppose A(-9, -8) and B(-4, -6). What is the x coordinate of the midpoint for AB?

A:

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

A: Consider the point A(4, - 3) which is 6 units from the point B(0,y).

Q: points

A: Please refer to the image below

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

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 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 collection of points for which the distance to (12, 0) is twice the…

A: Refer to the question we need to find an equation for the collection of points for which the…

Q: Find an equation of the set of all points equidistant from the points A(-3,

A: Given, the coordinate points A-3, 6, 2 and B5, 2, -3.

Q: Find the distance between the following two points: (-1, -2) and (-1, 3)

A:

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 point on the line y = 4x + 3 that is closest to the origin. (х, у) -

A:

Q: Plot each pair of points and compute the distance between them:(a) (0, 0) and (-2, 3) (b) (-3, -3)…

A:

Q: What point on the line y=3x+6 is closest to the​ origin?

A: The point on the line closest to the origin is the foot of perpendicular drawn from origin to the…

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: Write an equation for a line perpendicular to f (1) = 5x – 1 passing through the point (5, 20). %3D…

A:

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

A:

Q: Find the slope of x²y=8 at the point (2,2).

A: Given: x2y=8 To find: Slope of x2y=8 at (2,2)

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 .

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.