Question

The center of a hyperbola is (-5,8). The length of the conjugate axis is 6 units, and the length of the transverse axis is 14 units. The transverse axis is parallel to the y axis.
What is the equation of the hyperbola in standard form?

Answer 1

Answer:

$(\frac{x+5}{3}) ^{2}+ (\frac{y-8}{7} )^{2} =1$

Step-by-step explanation:

• IMPORTANT FORMULA: the standard equation of a hyperbola whose transverse axis is parallel to the y axis is:

$(\frac{x-h}{a}) ^{2}+ (\frac{y-k}{b} )^{2} =1$

where, (h,k) : center  of the hyperbola

a : semi conjugate axis [ length of conjugate axis/2]

b: semi transverse axis [ length of transverse axis/2]

• so, here a=3, b=7, [h,k]=[-5,8]

• by substituting these values in the above given formula,

• the equation of the hyperbola in standard form is :

$(\frac{x-(-5)}{3}) ^{2}+ (\frac{y-8}{7} )^{2} =1$

$(\frac{x+5}{3}) ^{2}+ (\frac{y-8}{7} )^{2} =1$