What is the asymptotes of ((x-1)^2)/4-((y+2)^2)/1 =1 ?

The asymptotes of ((x-1)^2)/4-((y+2)^2)/1 =1 is y= 1/2 (x-1)-2,\quad y=-1/2 (x-1)-2

Popular >

asymptotes of ((x-1)^2)/4-((y+2)^2)/1 =1

asymptotes

\frac{( x - 1 ) ^{2}}{4} - \frac{( y + 2 ) ^{2}}{1} = 1

y = \frac{1}{2} (x - 1) - 2, y = - \frac{1}{2} (x - 1) - 2

Solution steps

y = \pm \frac{b}{a} (x - h) + k

Calculate Hyperbola properties

\frac{( x - 1 ) ^{2}}{4} - \frac{( y + 2 ) ^{2}}{1} = 1 :

Right-left Hyperbola with

(h, k) = (1, - 2), a = 2, b = 1

y = \frac{1}{2} (x - 1) + (- 2), y = - \frac{1}{2} (x - 1) + (- 2)

\frac{x ^{2}}{4} - \frac{y ^{2}}{49} = 1

4 y^{2} - x^{2} = 900

9 (x - 1)^{2} - 16 (y + 2)^{2} = 144

9 x^{2} - y^{2} + 6 y - 18 = 0

4 x^{2} - y^{2} - 24 x - 6 y + 23 = 0

What is the asymptotes of ((x-1)^2)/4-((y+2)^2)/1 =1 ?
The asymptotes of ((x-1)^2)/4-((y+2)^2)/1 =1 is y= 1/2 (x-1)-2,\quad y=-1/2 (x-1)-2