Hyperbola Calculator
getcalc.com's hyperbola calculator is an online basic geometry tool to find the center, axis, eccentricity and asymptotes of Hyperbola, in both US customary and metric (SI) units.
Steps to Find Center, Axis, Eccentricity and Asymptotes of a Hyperbola
The step by step solution for how to find what is the center, axis, eccentricity and asymptotes of a Hyperbola.Solution :
step 1 Address the formula input parameter and values
x0 = 5
y0 = 4
a = 5
b = 4
step 2 Apply x, y, a and 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 and 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.
