Find an equation in standard form for the hyperbola with vertices at (0, ±10) and asymptotes at y = ±five divided by four times x..

The equation of hyperbola is .

Step-by-step explanation:

Given information: Vertices at (0, ±10) asymptotes at .

Vertices are on the y-axis, so given hyperbola is along the y-axis. The  standard form for the hyperbola is

where, (h,k) is the center of hyperbola. (0,±b) are vertex and are  asymptotes.

Vertices at (0, ±10), it means center of the hyperbola is (0,0). So the standard form for the hyperbola is

          .... (1)

Vertices of hyperbola:

On comparing we get

The value of b is 10.

Asymptotes of the hyperbola:

On comparing both sides, we get

Substitute b=10.

On cross multiplication,

Divide both sides by 5.

The value of a is 8.

Substitute a=8 and b=10 in equation (1) to find the equation of hyperbola.

Therefore the equation of hyperbola is .

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step-by-step explanation: