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

Q: Determine the angle between the curves 2x=y2 and x2+y2-5x=0

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

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

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

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Q: Explain the steps required to find the length of a curve y = ƒ1x2 between x = a and x = b.

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Q: Find the distance from the point to the line. (-4, – 2,1); x= 5 – t, y = 1- 2t, z = - 6 + 3t

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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 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 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 slope of the line tangent to the curve 5x3 + 2x5y − y2 = 2 at the point (1,3) Write your…

A: Explantion: Given that: 5x3+2x5y-y2=2 Concept: slope of line m=dydx dxndx=nxn-1 duvdx=udvdx+vdudx

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 segment tangent to the curve y−2x^2−1=0 which is parallel to the line…

A: Given curve is y-2x2-1 = 0

Q: The slope of the line tangent to the graph of 3x +5In y 12 at (2, 1) is 12 (A) 12 (B) 5. (C) 12 4.

A: Given that 3x2+5lny=12To find : Slope of the tangent line at point 2,1Solution :

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 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 distance from the point (0, 1, 3) to the line = 2t, y = 6–2t, z = 3+t

A: (0,1,3)    L=x=2t, y=6-2t, z=3+t

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

A: We have to solve

Q: Find the equation of the line tangent to 3x²y + 4xy2 = 6x² + 5y at the point (1,).

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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 | 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 A(4, 6, -3) to the line x = 3t + 1, y = -t + 3, z = 6t

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Q: Find the distance of the point (4, 2, -4) from the line r(t) = (1+2t, 1+ 2t, 7 - 3t).

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

A: Given query is to find the the distance between point and the line

Q: Find the point on the line y = 4x + 3 that is closest to the origin. %3D (x, y) = %3D -

A: Given query is to find the Indicated point .

Q: With center on the line y = 2x – 13 and tangent to the line y = - 3x + 57 at (16, 9)

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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 distance from the point (3, 2, 5) to the line 0, y = 2+ 2t, z = 5 + 2t.

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Q: The line y=3x+6 is tangent to the graph of y = (-48)/(x-6) at the point ?

A: The given equation of tangent is y=3x+6 and its tangent to graph of y=-48x-6. To find the points at…

Q: Show that the distance between the line 3x 4y + 3 = 0 and the point (1, –1) is 2. |

A: In this question, we have to prove that the distance between line and point is 2.

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 distance from the point (4, 9) to the line y = 2x.

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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 slope of * y+ Vx+ y =x at (3,1)

A: A detailed solution is given below

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 tangent to the parabola y = x^2 -1 at the point (-2,3).

A: Given the parabola :

Q: Find the equation of the line normal to x^3 + y^3 = 6xy at (3,3)

A: Given, x3+y3=6xy

Q: point

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

A: Let the point (x, y) on the given line x+2y=5  is closest to the origin (0, 0). observe that…

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

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Q: Determine the equation of the line parallel to y+1=0 and tangent to y = 3x – 5x + 4 -

A: Recall that the slope of the parallel lines is equal. And the slope of the tangent line at any point…

Q: Find x²z ds, where C is the line segment from (0,6,4) to (1,3,-2) C

A: ∫C y ds,  C: x=t2, y=t,  -2≤t≤3   dxdt = 2t,   dydt= 1∫Cy ds = ∫-23 t  (2t)2+1 dt=∫-23 t  4t2+1…

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 :