Question

What are the equations for the asymptotes of this hyperbola? Y^2/36 - x^2/121=1

Answer 1

Answer:

$\huge{\mathfrak{Solution}}$

$\huge{\bold{ \frac{ {y}^{2} }{36} - \frac{ {x}^{2} }{121} = 1 }}$

$\huge{\bold{ \frac{(y - k) {}^{2} }{ {a}^{2} } - \frac{(x - h) {}^{2} }{ {b}^{2} } = 1 \: is \: the \: standard \: equation \: with \: center \: (h ,k),semi-axis \: a \: and \: semi-conjugate \: -axis \: b.}}$

$\huge\boxed{\mathfrak{We \: get,}}$

$(h,k) = (0,0),a = 6,b = 11$

$For \: hyperbola \: assymtoms \: are \: y = + \frac{a}{b} (x - h) + k$

$Therefore,y = \frac{6}{11} (x - 0) + 0,y = - \frac{6}{11} (x - 0) + 0$

$\large\boxed{\bold{y = \frac{6x}{11},y = - \frac{6x}{11} . }}$

Answer 2

Set the equation to 0. new equation would be y^2/36 - x^2/121 = 0

factor the new equation: (y/6 + x/11)(y/6 - x/11) = 0

y/6 + x/11 = 0 —> y = -6x/11
y/6 - x/11 = 0 —> y = 6x/11

the asymptotes would be y = -6x/11, y = 6x/11