Q2) A- Find the distance between the line (y = x + 3 ) and center of circle (x²+y²–2x=0).

Q: Find the distance between the point (5, 1) and the line y = 3x + 1. O 3V10 O 7/10 O 9/10 O 5V10

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Q: What is the maximum vertical distance between the line y = x + 30 and the parabola y = x2 for -5 s x…

A: given, equation of line is y = x + 30 and equation of parabola is  we have to find maximum vertical…

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: Find the egmation for the Line" dhint passes through the point (,0) and parallel to the Line…

A: NOTE:Kindly repost the other question as a separate question.

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

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Q: Find the point on the line x/a + y/b =1  that is closest to the origin. Be sure to enter it as an…

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Q: 4. The midpoint of the line segment with endpoints (x1, yı) and (x2, y2) is given by the formula

A: we know, the midpoint of the line segment with end points (x1,y1) and (x2,y2) is given by the…

Q: How find the pistance from fant (1,3) and Line y -4

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Q: How do I do this?

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

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Q: Find the area of the triangle bounded by the lines y=x+3, y=2x-1 and y=-3x+4

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Q: What is the length of the part of the curve y squared = (x-1) between the points (1,0) and (2,1)?

A: To find- Length of the part of the curve.

Q: Find the length of the chord intercepted by the circle x2+y2-x+3y-22=0 on the line y=x-3

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Q: What is the maximum vertical distance between the line y = x + 6 and the parabola y x2 for -2 < x<…

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Q: A5: What is the minimum (perpendicular) distance from the point p = (-1,–2) to the line L := 4x = 14…

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Q: Use the Midpoint Formula three times to find the three points that divide the line segment joining…

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Q: Find the distance from the point (1, 2, 0) to the line æ = 3t, y= 1, z= 2 – t.

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Q: ` What is the shortest distance from the surface xy + 9x + z² = 76 to the origin? distance =

A: z2+9x+xy=76z2=76-9x-xy   ---- Eq 1Let P(x,y,z) be a point on the given surface. We know that…

Q: Find the equation of the line in standard form (i.e., y = mx + b) that conatins the point (-3,5) and…

A: We have to find the equation of line in standard form if it is passing through the point -3, 5 and…

Q: What is the maximum vertical distance between the line  y = x + 30  and the parabola  y = x2 for…

A: Definition used -                  Vertical distance is given by -…

Q: Two straight lines 3x – 2 y + 5 = 0 and 6x – 4y + 10 = 0 intersect at the origin. are coincident.…

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Q: Find the point on the line y = 3x + 5 that is closest to the origim %3D (x, y) = %3D

A: We have to solve

Q: The distance from a point (2, y) to the line 4x + 3y =0 is equal to 5. Find the value of y.

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

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Q: Find the acute angles between the intersecting lines x = 2 + t, y = 4t + 2, z = 1 + t and x = 3t -…

A: Given: The equation of lines x = 2 + t,  y = 4t + 2,    z = 1 + t      and x = 3t - 2,   y = -2,   z…

Q: d the eqation of the line that passes through A(1,2,1) and intersects the line x+1 у-2 z+1 %3D at…

A: Topic:- geometry

Q: By using the calculus of variations, prove that the shortest distance between two points in the y z…

A: The functionals with in the calculus of variations are of the form V[f(x)]=∫abF(x,y(x),y'(x))dx The…

Q: 9y? = 4x3 from the origin to the point (4, %3D 144. Identify the length of the curve

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Q: The coordinates of a point on the line x+ y+1 = 0 which is at a distance /2 units from the line 3x +…

A: Given: The line x+y+1=0 which is at a distance 2 units from the line 3x+4y-2=0 To find: Coordinates…

Q: Find the point on the line y = 3x + 2 that is closest to the origin. (х, у) %3D

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Q: How is the line y = 1 converted by mapping w = e? ?

A: In this question, we convert the line y=1 by mapping w=e^z.

Q: What is the maximum vertical distance between the line y = x + 2 and the parabola y = x2 for -1 <x<…

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Q: 2)What line is perpendicular to 2x + y = 3 at (1,1)?

A: What line is perpendicular to 2x+y=3 at (1,1)?

Q: Find the distance between the pointx1 =−1, y1 =1, z1 =3 and the point x2 =1, y2 =1, z2 =1.

A: The first point is (-1,1,3) and the second point is (1,1,1) We will use the distance formula:

Q: Find the length of the line segment described by, (x,y,z)=(1,2,1) +t(-1,5,4)), where 0<t<5.

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Q: How close does the semicircle y = V16 – x² come to the point (1, v5)? |

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Q: The area bounded by the curve y = 4x and the lines r = 6 ,x = 12 and a – axis is 144 square units O…

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Q: Find the shortest distance from the origin to the line of intersection of the planes 2x + y − z = 1…

A: Given: The planes: 2x+y-z=1 and x-y+z=2.

Q: Find the distance between the plances 3x + y – 4z = 2 and 3x + y – 4z = 24

A: Given the two planes 3x+y-4z=2,3x+y-4z=24. The distance between two planes Ax+By+Cz=d1,Ax+By+Cz=d2…

Q: find the distance from the point to the line (2, 2, 0); x = -t, y = t, z = -1 + t

A: Given information: The point to the line is (2, 2, 0) and x = -t, y = t, z = -1 + t. Calculation:…

Q: Show that f(-ydx + xdy) where C is the line segment joining (x, y) and (x₂, y2).

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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: In the standard (x,y) plane, what is the distance between (3, 4) and (6, 2)?

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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: 5- Find the distance from the point to the line. a. (0,0, 12); x = 4t, y = -2t, z = 2t b. (0, 0, 0);…

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Q: By using the calculus of variations, prove that the shortest distance between two points in the y z…

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Q: What is y = _ + x3 1 curve x = 1 and x = 2 the length of the part 12 х between the abscissa points?

A: We find dy/dx using the power rule

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

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Q: The distance between the line x =-2+2t ,y=2t+1, z=2-t and the line x=3- 2t ,y=-2t+1,z=t is

A: Distance between two Parallel Lines we calculate as a distance between intersection of the lines and…

Q: What is the maximum vertical distance between the line y = x + 6 and the parabola y = x< for -2 <x<…

A: To Find