SOLUTION: what is the standard form of x^2-4x-4y^2+8y-100=0

Question 451835: what is the standard form of x^2-4x-4y^2+8y-100=0
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
what is the standard form of x^2-4x-4y^2+8y-100=0
..
Completing the square is the first for finding out what kind of conic this equation is:
(x^2-4x+4)-4(y^2-2y+1)=100
(x-2)^2-4(y-1)^2=100+4-4=100
divide by 100
(x-2)^2/100-(y-1)^2/25=1
Standard form of a hyperbola with horizontal transverse axis: (x-h)^2/a^2-(y-k)^2/b^2=1, with (h,k) being the (x,y) coordinates of the center.
Standard form of a hyperbola with vertical transverse axis: (y-k)^2/a^2-(x-h)^2/b^2=1, with (h,k) being the (x,y) coordinates of the center.
Note that the only difference between the two forms is the interchange of (y-k)^2 with (x-h)^2.
..
Given hyperbola is of the first form with a horizontal transverse axis (hyperbola opens sideways) and center at (2,1).
a^2=100
a=10
length of transverse axis=2a=20
b^2=25
b=5
Length of conjugate axis=2b=10
RELATED QUESTIONS
What is the standard form of the equation x^2 + y^2 + 10x -8y +5 =... (answered by lwsshak3)

What is the equation in standard form for the circle:... (answered by Earlsdon)

What is the standard form of... (answered by MathLover1)

Write the equation of the circle in standard form and give the center and radius.... (answered by josgarithmetic,MathTherapy)

x^2-4y^2-4x+8y=0 (answered by lwsshak3)

What is " 2y^2 - 4y -x + 12 = 0 " in the standard form of a... (answered by lwsshak3)

What conic equation is represented here and give its standard form:... (answered by lwsshak3)

Please help me. transform this general form into standard form. 4x^2+4y^2+12x-8y+25... (answered by josgarithmetic)

what is the standard form of... (answered by solver91311,stanbon)