How do you find the standard form given #4x^2+9y^2-8x+54y+49=0#? Precalculus Geometry of a Hyperbola Standard Form of the Equation 1 Answer salamat Feb 24, 2017 #(2 x - 2)^2 + (3 y + 9)^2 = 36# Explanation: #4 x^2 + 9 y^2 - 8 x + 54 y + 49 = 0# #(2 x)^2 + (3 y^2) - 8 x + 54 y + 49 = 0# rearrange the equation, #[(2 x)^2 - 8 x] + [(3 y^2) + 54 y] + 49 = 0# #[(2 x - 2)^2 - 2^2] + [(3 y + 9^2) -9^2] + 49 = 0# #(2 x - 2)^2 + (3 y + 9^2) -4 -81 + 49 = 0# #(2 x - 2)^2 + (3 y + 9)^2 - 36 = 0# #(2 x - 2)^2 + (3 y + 9)^2 - 36 = 0# #(2 x - 2)^2 + (3 y + 9)^2 = 36# Answer link Related questions What is the standard form of the equation of a hyperbola? What conic section is represented by the equation #(y-2)^2/16-x^2/4=1#? What conic section is represented by the equation #y^2/9-x^2/16=1#? What conic section is represented by the equation #x^2/9-y^2/4=1#? How can I tell the equation of a hyperbola from the equation of an ellipse? What does the equation #9y^2-4x^2=36# tell me about its hyperbola? What does the equation #(x+2)^2/4-(y+1)^2/16=1# tell me about its hyperbola? What does the equation #(x-1)^2/4-(y+2)^2/9=1# tell me about its hyperbola? Why is a hyperbola considered a conic section? How do you write the equation of a hyperbola in standard form given Foci: (3,+-2) and... See all questions in Standard Form of the Equation Impact of this question 3149 views around the world You can reuse this answer Creative Commons License