Find an equation of the hyperbola such that for any point on the hyperbola, the difference...

Find an equation of the hyperbola such that for any point on the hyperbola, the difference between its distances from the points (5, 6) and (13, 6) is 6.

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milcah answered 2 years ago

An equation of a hyperbola is given. 25x2 − 16y2 = 400 (a) Find the vertices,...

An equation of a hyperbola is given. 25x2 − 16y2 = 400 (a) Find the vertices, foci, and asymptotes of the hyperbola. (Enter your asymptotes as a comma-separated list of equations.) vertex (x, y) = (smaller x-value) vertex (x, y) = (larger x-value) focus (x, y) = (smaller x-value) focus (x, y) = (larger x-value) asymptotes (b) Determine the length of the transverse axis. (c) Sketch a graph of the hyperbola.

question 11 a, b, and c a. Find the equation of the hyperbola satisfying the given...

question 11 a, b, and c a. Find the equation of the hyperbola satisfying the given conditions. Vertices at (-12, 0) and (12, 0); focus at (3squareroot 17, 0) b. Determine whether the given function is one-to-one. If it is one-to-one, find a formula for the inverse f(x)=6x-3/6x+3 c. Solve. How long will it take for $1600 to grow to $14,000 at an interest rate of 3.7% if the interest is compounded continuously? Round the number of years to the...

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.

1. Find the standard form of the equation of the hyperbola satisfying the given conditions. Foci...

1. Find the standard form of the equation of the hyperbola satisfying the given conditions. Foci at (-5,0) and (5,0); vertices at (1,0) and (-1,0). 2. Find the standard form of the equation of the hyperbola satisfying the given conditions. Foci at (0,-8) and (0,8); vertices at (0,2) and (0,-2).

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.

Find the center, vertices, foci, and the equations of the asymptotes of the hyperbola. (If an...

Find the center, vertices, foci, and the equations of the asymptotes of the hyperbola. (If an answer does not exist, enter DNE.) x2 − 2.25y2 + 22.5y − 92.25 = 0

Find the equation of the tangent line to the curve at the point corresponding to the...

Find the equation of the tangent line to the curve at the point corresponding to the given value of t 1. x=cost+tsint, y=sint-tcost t=7pi/4 2. x=cost+tsint, y=sint-tcost t=3pi/4?

a.) Find the shortest distance from the point (0,1,2) to any point on the plane x...

a.) Find the shortest distance from the point (0,1,2) to any point on the plane x - 2y +z = 2 by finding the function to optimize, finding its critical points and test for extreme values using the second derivative test. b.) Write the point on the plane whose distance to the point (0,1,2) is the shortest distance found in part a) above. All the work necessary to identify this point would be in part a). You just need to...

a) Find the equation of the normal line at the point (−2, 1 − 3) to...

a) Find the equation of the normal line at the point (−2, 1 − 3) to the ellipsoid x2 /4 + y2 + z2 / 9 = 3 b) Find a plane through P (2, 1, 1) and perpendicular to the line of intersection of the planes: 2x+y−z = 3 and x+2y+z = 2.

a) Find an equation of the plane tangent to the graph of f at the given point P.

a) Find an equation of the plane tangent to the graph of f at the given point P. Write your answer in the form ax + by +cz= d, where a, b, c, and d are integers with no common factor, and a is greater or equal to 0. f(x,y)= 2x3y + 4x-y, P(1,3,7) b) Use a multivariable chain rule to find a formula for the given derivative or partial derivative. w= f(x,y), x=g(u,v), y=h(u,v); ∂w/ ∂v

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