Hyperbola Center, Axis, Eccentricity & Asymptotes Calculator
getcalc.com's hyperbola calculator is an online basic geometry tool to calculate center, axis, eccentricity & asymptotes of hyperbola shape or plane, in both US customary & metric (SI) units.
Steps to Find Center, Axis, Eccentricity & Asymptotes of a Hyperbola
The step by step workout for how to find what is the center, axis, eccentricity & asymptotes of a hyperbola.workout :
step 1 Address the formula input parameter and values
x0 = 5
y0 = 4
a = 5
b = 4
step 2 Apply x, y, a & b values in F (x, y) formula
F(x, y) = (x0 + √a² + b² , y0)
= (5 + √5² + 4² , 4)
= (5 + √25 + 16 , 4)
= (5 + √41 , 4)
= (5 + 6.4031 , 4)
F(x, y)= 11.4031, 4
step 3 Apply x, y, a and b values in F’ (x, y)
F’ (x, y) = (x0 - √a² + b² , y0)
= (5 - √5² + 4² , 4)
= (5 - √25 + 16 , 4)
= (5 - √41 , 4)
= (5 - 6.4031 , 4)
F’ (x, y)= -1.4031, 4
step 4 Apply a and b values in eccentricity formula
Eccentricity = √a² + b²
= √5² + 4²
= √41
Eccentricity = 6.4031
step 5 Apply the values a, b, x0, y0 in asymptotes H’L formula
Asymptotes H’L = b/ax + (y0 - b/ax0)
= 4/5x + (4 - 4/55)
= 0.8x + (4 - (0.8 x 5))
= 0.8x + (4 - (4))
Asymptotes H’L = 0.8x + 0
step 6 Apply the values a, b, x0, y0 in asymptotes L’H formula
Asymptotes L’H = -b/ax + (y0 + b/ax0)
= 4/5x + (4 + 4/55)
= -0.8x + (4 - (-0.8 x 5))
= -0.8x + (4 - (-4))
Asymptotes L’H = -0.8x + 8
Hyperbola & Formulas
Hyperbola is a geometric shape represents the open curve with two symmetrical intersection of cone having same vertexes pointing each other on the same axis.
