Find the distance from the point (3, 9) to the line y = 2x.

Q: Find the point on the line y=x that is closest to the point (3, -1)    The point is (___ , ____)

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Q: Find the point on the line x /a + y/ b = 1 that is closest to the origin.

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Q: Find the shortest distance from the point x = (-3, 0, -12)  to the line r = t(0, -2, -2).

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Q: Perpendicular to the line y=−1/2x+1 containing the point (3,6)

A: Solution is done in step 2

Q: Find the points of intersection of the line y = 5 x with the curve y = 3 x + x^2

A: In order to find the point of intersection of given line line and curve , we must find values where…

Q: Where is the line y = 10 – 2x closest to the origin? (х, у) %3D

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Q: Find the distance between the points (3,6) and the line x - 2y +3 =0.

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Q: Find the distance from the point to the line.

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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 slope of the curve at the point indicated.

A: We need to find the slope of the curve at the point indicated, y=5x-3x2,x=1

Q: Find the distance of the point (3, 2, –4) from the line r(t) = (1+ 3t, –1+ 2t, 3 – 3t).

A: for finding distance of the point3,2,-4 from line rt=1+3t, -1+2t, 3-3t we assume a point1+3t, -1+2t,…

Q: Find the distance from the point to the given line x 1+t, y= 3-2 2t, z=4- 3t and point (4,1,-2)

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

A: Explanation of the answer is as follows

Q: Find the distance from the point to the given line. (0, 1, 2); x= 2t, y = 5 – 3t, z = 2 + t %3D

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Q: Find the distance from the point to the line. Knowing that the point Po (2, 1, 3), x= 2+2t, y= 1+6t,…

A: The distance of a point P from a line passing through the point Q and parallel to the vector v→ is…

Q: Find the distance from the point S(0,0,12) to the line L: x = 4t , y = -2t z = 2t 3

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Q: Find the distance from the point (4, 21) to the line y = 5x

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Q: Find the distance between the point (−3, 5, 1) and the line given by x = 1 + t, y = 5 − 2t, and z =…

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Q: Find the distance between the point (-1, 5, 3) and the line given by x = 5 + t, y = 1 - 2t, and z =…

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Q: Find the distance from the point S= (1, 2, 1) to the line x = 2-t, y=-1+2t, and z=2+ 2t.

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Q: Find the distance from the point (3,-1, 4) to the line a = 4 – t, y = 3 + 2t, z = -5+ 3t.

A: Given: point 3,-1,4 and equation of line x=4-t, y=3+2t, z=-5+3t Formula: The distance between point…

Q: Find the distance from the point P(2,1) to the line v = x + 2

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Q: Find | xz ds, where C is the line segment from (0,0,-6) to (-5,5,-7)

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Q: Find the distance from the point S(0,0,12) to the line L: x = 4t , y=-2t z = 2t

A: Write the vector of the given line using x=4t, y=-2t, and z=2t. L→=xi→+yj→+zk→   =4ti→+-2tj→+2tk→…

Q: find the distance from A(4, 6, -3) to the line x = 3t + 1, y = -t + 3, z = 6t

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Q: Find the angle formed by the line 3x+4y-12=0 with the x-axis.

A: Angle of the line along x-axis

Q: The slope of the line tangent to the circle x' + y = 100 at the point (- 6,8)is

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

A: Find the point on the line y = 4x +5 that is closest to the origin. (x,y) = ____

Q: Find the distance from the point (4, 3, 0) to thea. x-axis b. y-axis c. z-axis

A: It is given that, the point 4,3,0.We have to find the distance from the given  point to the a…

Q: Find a point on the line y = 2x 3 that is 5 units from the x axis. %3D

A: The given equation is, y=2x-3

Q: Find the smallest angle between the lines 2x+y-8=0 and x+3y+4=0

A: We have to find angle between lines.

Q: Q7// Find the distance between line L1:y=2 x+6 and circle with .center (1,2) and radius 2

A: The distance between the circle and the line is equal to the perpendicular distance between the…

Q: Find the distance from the point to the line. Knowing that the point Po (2, 1, 3), x= 2+2t, y= 1+6t…

A: This question is based on distance between point and line in 3d geometry.

Q: Find the distance from the point (1,–4,2) to the line x=2+t, y =-2+2t, z = 4 –t Try not to use any…

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Q: Find the distance from the point (4, 3, 0) to the y-axis

A: We have to find the distance from the point 4, 3, 0 to the y-axis. We know that distance from the…

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

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Q: Find the midpoint of the line segment joining the points P1 and P2 . Equation: y3 = x + 1Points: (1,…

A: Given y3=x+1 Points: (1, 2); (0, 1); ( - 1, 0)

Q: Find xz ds, where C is the line segment from (0,-2,4) to (0,-6,1).

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

A: Given,         y=13x2+232

Q: Find a distance from the point S(1,1,5) to the line x=1+t, y=3-t,and z= 2t

A: We need to find the distance of the point (1,1,5) and the given line.

Q: Find the distance between the line x + y + 2 = 0 and the point (1, 1).

A: The distance between the line ax+by+c=0 and the point x1,y1 is given as below. d=ax1+by1+ca2+b2

Q: Find the distance from the point (1,1,5) to the line X=1+t, Y=3-t, Z=2t. *

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Q: 19. Find the point on the line y= 2x + 3 that is closest to the origin.

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Q: Find the distance from the point (-3,1,0) to the line d(t) = (1, 0, 2)t + (4, – 9, – 2) .

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Q: Find the distance between the parallel lines.

A: Here x1 = 1; x2 = 0; y1 = 0; y2 = 1; z1 = -1; z2 = 1

Q: Find the distance between the point (-1, 3, 5) and the line given by x = 3 + t, y = 1- 2t, and z =…

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Q: Find the angle between the lines y-V3x-5=0 and 3y-x+6=0.

A: Introduction :

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.