Let H be the segment of the hyperbola x-y°= | Connecting (1,0) to (2, J3). Evaluate the line, integral %3D Suly dx t x dy

Q: Find the coordinnates of a point on the oarabola y\power{2}=8x whose focal distance is 4.

A: Parabola.  y2=8x.  and Focal distance = 4

Q: Differentiate the following hyperbolic functions

A: Consider the given hyperbolic function y=log5sinh e9x2.

Q: Calculate the distance from point A(1, 2, 1) to the plane of equation 3x-4y + 5z = 1.

A: To find distance of point to plane using the formulae: Given point is and plane equation is .

Q: Show that the tangent lines at the points where the ellipse x² – xy + y² = 3 cross the x-axis are…

A: Explained below

Q: Find the equation of the tangent plane to the surface 2= 42 + 3y+7zy at the point (0,-1,3).

A:

Q: * Find the equation of the tangent plane to the surface 9a2²-12xy = 5x2+5 at the ivon Ni Smob point…

A:

Q: Evaluate Szdz where y traces the arc of the parabola y = x² from (1,1) to (2,4).

A:

Q: Find the distance between the point (p, 4p) and the parabola y? = 2px, where p is a fixed positive…

A: let the point on parabola be A= (x, y)  B = (p, 4p) Thus,  AB = x-p2+y-4p2 but parabola is y2=2px…

Q: 6. What is the equation for the slope of the ellipse+= 1 at (x₁, yi)? A. B. C. D. E. y' = y' = b²y₁…

A: We have to find the equation of the slope of ellipse at the point (x1,y1).

Q: Find y in terms of x. dy = x 2 + 5, curve passes through (0, 14) dx x3 A) y = + 5x 3 B y = x3 + 5x +…

A:

Q: Q2/ Find the Parametric aned standand equatior of the line Hhat passer through Points (-2,1,0)…

A: The equation of line passing through given two points is given as follows:

Q: Parametrize y = -x2 + 4 in terms of u and v %3D

A:

Q: Find dy/dx: y = In [(1 + t^2)/(1 - t^2)]

A:

Q: Find the curve y if dy = x2 +5, dx + 5, curve passes through (0, 25)***

A:

Q: Find the distance between the skew lines with parametric equations x=3+t, y=2+6t, z = 2t, and…

A: Given :x=3+ty=2+6tz=2tx=2+2sy=4+14sz=-2+5s

Q: Find the distance between the skew lines with parametric equations x = 3 + t, y = 1 + 6t, z = 2t,…

A: I am attaching image so that you understand each and every step.

Q: Find the equation of the tangent plane to the surfaceln(x3 + y3 + z3) = x2z + 1at the point (1, 1,…

A: The objective of this question is to find the equation of the tangent plane to the given surface at…

Q: The locus of the foot of the perpendicular from the centre of the hyperbola xy = c² on a variable…

A: Given hyperbola equation is  xy = c2 The parametric form of this hyperbola is  x = c t  and   y =…