The coordinates of a point on the line x+ y+1 = 0 which is at a distance /2 units from the line 3x + 4y-2 0 are

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

A:

Q: find the distance from the point (2,5) to the line y=2x.

A: Refer  to the question,The distance from a point to the line is the shortest distance between the…

Q: The distance between the line x - y + 3 = 0 and the line y = x + 2 is

A: The given two lines are x-y+3=0  and y=x+2. The equation of second line can be written as x-y+2=0.…

Q: Find the equations of both lines that are tangent to the curve y = x - 3x2 + 3x - 3 and are parallel…

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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: The line represented by 3x-4y=16 is dilated by a scale factor of 3 centered at the origin. Which…

A: The dilation is the way of transformation. Every parent figure can be dilated by a scalar factor. By…

Q: Find the point on the line 5x + y = 5 that is closest to the point  (−4, 1).   x,y= (  , )

A:

Q: the distance from the point (5,3) to the line 2x+4y+5=0 is

A: solution

Q: Find the point on the line 4x + y = 7 that is closest to the point  (−4, 2).

A: Let P(x,y) be the point on 4x+y=7 y=7-4x Distance   D2=x+42+y-22Z=x+42+7-4x-22Z=x+42+5-4x2

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

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Q: Find the distance between the point P(-2,4) and the line 3x-4y 12

A: Find the distance from the point P (–2, 4) to the line 3x – 4y = 12.

Q: Find the equation of the line through point (2, 1/2, -3) and is perpendicular to the plane -x+4y+3z…

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Q: find an equation of a tangeant line to the curve at the given point y=4.9x-x^2, (5,-0.5)

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Q: Find the distance of the line 4x + 7y+ 5 = 0 from the point (1, 2) along the line 2x - y= 0.

A: Consider the provided question, (21) First find the intersection point of the two lines,

Q: Find an equation of the line containing the point (4,5) and parallel to the line 2x+5y=-3

A:

Q: Find the line L, that passes through the point P(-2,2) and perpendicular to the line L2: 2x+y=4.

A: We need to find equation of line L1 passing through (-2,2) and perpendicular to line L2 : 2x+y=4

Q: An object is traveling along a path described by y = x + 3. Where along that path will the object be…

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Q: Find an equation of the line L.   L is perpendicular to y=3x through point (2,6)

A: Compare y=3x with y=mx+bSo, m=3Slope=3

Q: find the distance from the point to the line. (3, -1, 4); x = 4 - t, y = 3 + 2t, z = -5 + 3t

A: Given Data The points is 3,-1,4. x=4-t. y=3+2t. z=-5+3t.   The line is passes through the points of…

Q: Find the'equation of the line that is perpendicular to y = -2x + 1 and contains the point (8, 2). =…

A: We are given the line y = -2x+1. And the slope of the above line is -2. So, the slope of the line…

Q: Find equations of both lines through the point (2, - 3) that are tangent to the parabola y = x2  + x…

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Q: Find the point on the line y = x + 1 that is closest to the point (4, 1).

A: The given equation of the line is, y=x+1 Let the point x,x+1 is closest to the point 4,1 Using…

Q: Find | x²z ds, where C is the line segment C from (0,-3,2) to (-3,-2,8)

A: Given C is the line segment from (0,-3,2) to (-3,-2,8) Now write the parametric equation for C…

Q: Find the distance from the point (0, 0, 0) to the line x = 5 + 3t, y = 5 + 4t, z = -3 – 5t.

A: Find the distance.

Q: What is an equation of the line that passes through the point (–6, –6) and is paralle to the line x…

A:

Q: Find the point on the line 3x + y= 9 that Is closest to the point (-5, 1). (x, Y) - (

A: According to question given that Line 3x+y=9, closest to the point (-5,1)We have to calculate the…

Q: Find the distance between the line 3x − y = 0 and the point (2, −4).

A:

Q: Find the distance between the point (−3, 1) and the line 4x + 3y + 4 = 0.

A: Given standard equation of line 4x+3y+4=0 and a point (-3,1)

Q: Find an equation of the line passing through the point (2,1) that is perpendicular to the line…

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Q: The line perpendicular to y=-x+1, passing through the point (–4, 2)

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Q: an equation for line L in point-s erpendicular to y 5x. 6Ty=5x (1,5) 2- -4 -2 4 6 2.

A: We will solve the problem

Q: Find the equation of th line perpendicular to the line 3y=2-4x and passing through the point (4,7)

A:

Q: Find the equation of a line passing through point (3,-2) and perpendicular to the line 2x + 3y + 4 =…

A: We are given that the line is passing through the point (3,-2) and perpendicular to the line…

Q: Find the point on the line 3x + 3y - 3 = 0 which is closest to the point (-2, 1). )

A: To find closest point on the line, draw perpendicular from the given point to the given line. The…

Q: Find the equation of line L through the point (5, 7/2, 5) intersecting at right angle the line M…

A: Given that, the line L is passing through the point 5,72,5 intersecting at right angle the line M…

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 equation of a line that is parallel to y = 3/2x + 1 and passes through the point (-2, 1).

A: To find the equation of a line that is parallel to y=32x+1 and passes through the point -2, 1.

Q: The line y = 3x+7 and the curve xy-x = 4 intersects at the points A and B Show that the equation to…

A: Given Data: Equation of the line: y=3x+7 ......(1) Equation of the curve: xy-x2=4 ......(2) The line…

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

A: This question is based on straight line intersection.

Q: Find the point on the line 6x + y = 7 that is closest to the point (−4, 2).  (x,y)=

A:

Q: What is an equation of the line that passes through the point (2, 2) and is parallel to the line x –…

A: Topic:- equation of line

Q: find the length of the curve y = 2x6+1/8x2 from x is greater than or equal to 1 and less than or…

A:

Q: Find the distance between the point (2, 9) and the line y = 3x + 4

A: Find the distance between the point (2, 9) and the line y = 3x + 4 To find the distance between a…

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

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Q: Find the equation of the Line passing through the point (2,-4,1) and parallel to the plane 3x+y-2z=5…

A: Given plane , 3x+y-2z=5 -i whose directionof the normal to the plane is3,1,-2and given equation of…

Q: point

A:

Q: What is the equation of a line that goes through the point (0, 2) and has a sloj y = - x + 2 y = 2x…

A:

Trigonometric Identities

Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.

Inverse Trigonometric Functions

Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec). When trigonometric ratios are calculated, the angular values can be calculated with the help of the inverse trigonometric functions.