Common tangent equation of y2 = 16x parabola and x2/36 - y2/20 = 1 hyperbola you...

Common tangent equation of y² = 16x parabola and x²/36 - y²/20 = 1 hyperbola you find.

Expert Solution

milcah answered 2 years ago

The equation of parabola is x2 = 4ay . Find the length of the latus rectum...

The equation of parabola is x2 = 4ay . Find the length of the latus rectum of the parabola and length of the parabolic arc intercepted by the latus rectum. (a) Length of latusrectum : 4a; Length of the intercepted arc : 4.29a (b)Length of latusrectum: —4a; Length of the intercepted arc : 4.39a (c) Length of latusrectum: —4a; Length of the intercepted arc : 4.49a (d) Length of latusrectum: 4a; Length of the intercepted arc : 4.59a

An equation of a hyperbola is given. y^2/36 - x^2/64 = 1 (a) Find the vertices,...

An equation of a hyperbola is given. y^2/36 - x^2/64 = 1 (a) Find the vertices, foci, and asymptotes of the hyperbola. (Enter your asymptotes as a comma-separated list of equations.) vertex (x, y) = (smaller y-value) vertex (x, y) = (larger y-value) focus (x, y) = (smaller y-value) focus (x, y) = (larger y-value) asymptotes (b) Determine the length of the transverse axis. (c) Sketch a graph of the hyperbola.

Consider the parabola y=1-x^2. Find the point on the parabola for which the tangent line through...

Consider the parabola y=1-x^2. Find the point on the parabola for which the tangent line through that point creates a triangle in the 1st quadrant and that triangle has minimum area.

The equation of an ellipse is x2/a2+y2/b2=1, where a and b are positive constants, a ³...

The equation of an ellipse is x2/a2+y2/b2=1, where a and b are positive constants, a ³ b. The foci of this ellipse are located at (c, 0), and (-c, 0), where c = (a2 – b2)1/2. The eccentricity, e, of this ellipse is given by e=c/a, while the length of the ellipse’s perimeter is \int_0^((\pi )/(2)) 4a(1-e^(2)sin^(2)\theta )^((1)/(2))d\theta . If 0 < e < 1, this integral cannot be integrated in terms of “well-known” functions. However, fnInt, may be used...

Consider the unit sphere x2 +y2 +z2 = 1 and the cone (z+√2)2 = x2 +y2....

Consider the unit sphere x2 +y2 +z2 = 1 and the cone (z+√2)2 = x2 +y2. Show that these surfaces are tangent where they intersect, that is, for a point on the intersection, these surfaces have the same tangent plane

Parametrize the osculating circle to the parabola y = x2 at x = -1

Let S be the surface with equation x2+y2-z2=1. (a) In a single xy-plane, sketch and label...

Let S be the surface with equation x2+y2-z2=1. (a) In a single xy-plane, sketch and label the trace curves z=k for k = -2,-1,0,1,2. In words describe what types of curves these are and how they change. (b) In a single yz-plane, sketch and label the trace curves x=k for k= -2,-1,0,1,2. In other words, describe what types of curves these are and how they change as k varies.

Find the equation of the hyperbola with: (a) Foci (1, −3) and (1, 5) and one...

Find the equation of the hyperbola with: (a) Foci (1, −3) and (1, 5) and one vertex (1, −1). (b) Vertices (2, −1) and (2, 3), and asymptote x = 2y. Consider the set of points described by the equation 16x2 −4y2 −64x−24y+19=0. (a) Show that the given equation describes a hyperbola and find the center of the hyperbola. (b) Determine the equations of the directrices as well as the eccentricity.

If C is the part of the circle (x2)2+(y2)2=1(x2)2+(y2)2=1 in the first quadrant, find the following...

If C is the part of the circle (x2)2+(y2)2=1(x2)2+(y2)2=1 in the first quadrant, find the following line integral with respect to arc length. ∫C(8x−6y)ds

Si U=(x2+y2+z2)-1/2 , demuestre que ∂2U/∂x2+∂2U/∂y2+∂2U/∂z2=0

Question