Graph of equation

Question

y^2 - x^2 = 144?

Answer 1

  The conic equation is y ²  - x ²  = 144

The coefficients of x ² and y ² are of opposite sign then it will be a hyperbola equation.

Write the above equation in standard form.

(y ²)/144 - (x ²)/144 = 144/144

y ²/12²  - x ²/12²  = 1

(y  - 0)²/12²- (x  - 0)²/12²= 12² 

Compare it to  standard form of vertical hyperbola is

"a " is the number in the denominator of the positive term

center: (h, k ) Vertices: (h , k + a ), (h, k - a)

Foci: (h , k + c ), (h , k - c )

Asymptotes of hyperbola is

In this case a  = 12, b  = 12

Center ( 0, 0)

Vertices (0, 12),(0, -12)

c  = √(a ² + b ²)

c  = √(12² + 12²) = √(288)

c  = 16.97

Foci : (0, 16.97), (0, - 16.97)

Asymptotes are y  = ±(12/12)(x  - 0) + 0

y  = ± x

y  = x  and y  = - x  are asymptotes.

Graph

Draw the coordinate plane.

Plot the center of hyperbola (0, 0).

To graph the hyperbola go 12 units up and down from center point and 12 units left and right from center point(since a = 12, b = 12.)

Use these points to draw a rectangle .

Draw diagonal lines through the center and the corner of the rectangle. These are asymptotes.

Plot the vertices and foci of hyperbola.

Draw the curves, beginning at each vertex separately, that hug the asymptotes the farther away from the vertices the curve gets.

The graph approaches the asymptotes but never actually touches them.