The minimum and maximum distances from a point P to a circle are found using the line determined by the given point and the center of the circle. Given the circle defined by x2 + y2 = 9 and the point P(4, 5), a. Find the point on the circle closest to the point (4, 5). b. Find the point on the circle farthest from the point (4, 5).

Q: Which of the following points lies on the circle (x-2)2 + (y-3)2 5? Select one: a. (3,5) b. (5, 3)…

A:

Q: a. (x - 2) 2 + (y - 2) 2 = 40 b. (x - 2) 2 + (x + 2) 2 = 34 10. If the equation of the circle is x2…

A:

Q: Find the center and radius of a circle defined by the equation 2x + 2y? + 10x – 6y + 55 = 0. Sketch…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: If the point A (4,3) and B(x,5) are on the circle with centre O (2,3). Find the Value of x

A:

Q: Find the center and the leneth of the diameter of the circle whose diameters endpoints are (0,-4)…

A: End points of diameter of circle are -  (0, -4) and (7,8)

Q: Find the equation of the circle if its diameter has an end points of (6, 1) and (-2, 3)

A: Suppose A6 , 1  and  B-2 ,3 be the endpoints of the diameter, O be the center and r be the radius of…

Q: Five minutes after the earthquake occurred, there was an aftershock. Determine the equation of the…

A:

Q: If the point A (4,3) and B(x,5) are on the circle with centre 0 (2,3). Find the Value of x

A:

Q: A

A:

Q: If the point A (4,3) and B(x,5) are on the circle with centre O (2,3). Find the Value of x

A: Distance between two points is d=x2-x12+y2-y12

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.