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

Q: 14. What is the slope of the curve at the point (0, x²+y-12r +4y = 5 %3D 0-2

A:

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

A:

Q: b. Enclosed by the curves y² = 4x + 4 and the line y = 4x – 16.

A:

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

A:

Q: 15. Find the point on the line y 3x that is closest to the point (50,0).

A:

Q: For what values of a and b is the line 5x + y = b tangent to the parabola y = ax? when x = 4?

A: y=ax2y'=2axy'(4)=2a(4)y'(4)=8a Now we have 5x+y=b ⇒y=-5x+b Compare with the equation y=mx+b From…

Q: How do I do this?

A:

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

A:

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: When is the line ax+ by = c parallel to the y-axis? To the x-axis?

A: ax+by+c=0        When a=0, then the line equation becomes               bx+c=0…

Q: The point (a,b) and (c,d) are points on the graph of y= x3+5 whose tangent lines are perpendicular…

A: y=x3+5slope at a,b =2x2=2a2     ...(1)slope at c,d =2x2=2c2     ...(2)slope of given line = -13…

Q: d is reflected over the line y =

A:

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: The distance of the line 7x + y –5 = 0 from the origin is?

A:

Q: 23. The distance from a point (2, y) to the line 4x + 3y =0 is equal to 5. Find the value of y. O…

A: Given that the distance from a point 2,y to the line 4x+3y=0 isequal to 5. We need to find the value…

Q: 16) Identify the hortizontal line. A) y=x C) y=-5 E) x= 4 B) x -y 1 D) x+y 0

A: Line Parallel to x axis

Q: 7. By definition find the slope of curve y = x2 – 2x – 3, at P(2, 3).

A:

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.

A:

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

A:

Q: Determine the length of the curve x = 3y2 -1 between y = 0 and y = 4 3/2

A: The given curve is x=3y32-1 We will find the arc length of the curve between y=0 and y=4

Q: roblem 4.1 Find the point on the line y = 2x + 3 that is closest to the origin.

A:

Q: (b) the curve x = = y²-y-6 and the line x = = 2y + 4;

A: Given; x=y^2-y-6, x=2y+4

Q: 1. Find the point on the line y = x nearest to the point (4, 1).

A: Since, we have been asked to solve part(i) which aims to findthe point on the line y=x nearest to…

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: End the Vellue of g) if the slope of the Curve y= x-2x is (2)?

A:

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: 4) Evaluate , -dz, where y is the line from 1 → 1+ i

A: In complex integration, we have to convert our given question into complex terms. But in our…

Q: 2 Show that the line y = x +3x+m for all values of m. y= mx+4 will touch or intersect the curve

A:

Q: Find the point on the curve y = √x closest to the point (2,2)

A: Here we have to find the point on the curve y = sqrt (x) closest to the point (2, 2)   use the…

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: 2- The distance d from the point R=(1,4,-3) to the line L: x=2+t,y%3-1-t Z- 3t is 4.43 False True

A:

Q: At what points will the line y=x intersect the unit circle x2  + y2 =1?

A:

Q: Find the distance between lines x + 3y = 5 and x + 3y = 25.

A: The distance between two parallel lines can be calculated using the formula,

Q: For what values of a and b is the 2x + y =b  line tangent tothe parabola y =ax2 when x =2?

A: Rewrite the equation of the tangent line as y=-2x+b and its slope is -2.

Q: i) Find the exact length of the curve x5 1 15 4x3 y= + 1 < x < 2,

A:

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: For what values of a and b is the line 4x+y=b4x+y=b tangent to the curve y=ax3y=ax3 when x=5x=5? a=…

A:

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: 9. What point on the line y=3x+4 is closest to the origin?

A: Given that: y=3x+4

Q: 13. Evaluate (2x + y + 3z) ds, where C is the straight line from (0, 1, 1) to (1,0, 1).

A: we have to evaluate

Q: B. Find the point on the line y = 10 – 2x that is closest to the origin. REFLECTION

A:

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

A:

Q: Suppose that dy xy + x d.x and that the point (5,0) lies on the graph of (x, y). What is the value…

A:

Q: Suppose the curve y =x4 +ax3+ bx2+ cx +d has atangent line when x=0  with equation y= 2x +1 and…

A: Given the curve is   y =x4 +ax3+ bx2+ cx +d Differentiating with respect to "x" y' = 4x3 + 3ax2 +…

Q: 16. If the lines y = 3x + 1 and 2y = x + 3 are equally inclined to the line y = mx + 4. Find the…

A:

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: 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