Answer:
The vertices are (12 , -5) , (-6 , -5)
The foci are (18 , -5) and (-12 , -5) ⇒ 2nd answer
Step-by-step explanation:
The standard form of the equation of a hyperbola with center (h , k) and transverse axis parallel to the x-axis is [tex]\frac{(x-h)^{2}}{a^{2}}-\frac{(y-k)^{2}}{b^{2}}=1[/tex] , where
- The coordinates of the vertices are (h ± a , k)
- The coordinates of the foci are (h ± c , k), where c² = a² + b²
∵ The equation of the hyperbola is [tex]\frac{(x-3)^{2}}{81}-\frac{(y+5)^{2}}{144}=1[/tex]
- Compare it with the form above
∴ h = 3 and k = -5
∴ a² = 81
- Take √ for both sides
∴ a = ± 9
∴ b² = 144
- Take √ for both sides
∴ b = ± 12
∵ Its vertices are (h + a , k) and (h - a , k)
∵ h + a = 3 + 9 = 12
∵ h - a = 3 - 9 = -6
∵ k = -5
∴ Its vertices are (12 , -5) , (-6 , -5)
∵ c² = a² + b²
∴ c² = 81 + 144
∴ c² = 225
- take √ for both sides
∴ c = ± 15
∵ Its foci are (h + c , k) and (h - c , k)
∵ h + c = 3 + 15 = 18
∵ h - c = 3 - 15 = -12
∵ k = -5
∴ Its foci are (18 , -5) and (-12 , -5)
