Question

What is the length of latus rectum hyperbola 16y^2-9x^2=144.​

Answer 1

Answer:

General Form or Equation of a Hyperbola is:

$\boxed{\bf{\dfrac{y^2}{a^2} - \dfrac{x^2}{b^2} = 1}}$

According to the question, the equation of the given hyperbola is:

⇒ 16y² - 9x² = 144

Dividing both LHS and RHS by 144, we get:

$\implies \dfrac{16y^2}{144} - \dfrac{9x^2}{144} = \dfrac{144}{144}\\\\\\\implies \dfrac{y^2}{9} - \dfrac{x^2}{16} = 1$

Comparing the above equation with the general equation, we get:

⇒ a² = 9 and b² = 16

⇒ a = ± 3 and b = ± 4

The formula to calculate the length of the Latus Rectum is:

$\boxed{ \bf{ \textbf{Length of L.R.} = \dfrac{2b^2}{a}}}$

We know that, the value of b² is 16 and value of a is +3. (Since a cannot be negative). Hence, substituting the given information we get:

$\implies \text{Length of L.R.} = \dfrac{2 \times 16}{3}\\\\\\\implies \boxed{ \bf{\textbf{Length of L.R.} = \dfrac{32}{3}}}$

Hence the length of the Latus Rectum is 32/3 units.

Answer 2

Answer:

Question :-

• What is the length of latus rectum hyperbola

$16 {y}^{2} - 9 {x}^{2} = 144$

Answer :-

• $\frac{32}{3} \: is \: the \: \: length \: of \: lactus \: rectum \: hyperbola$

Given :-

♧$16 {y}^{2} - 9 {x}^{2} = 144$

To prove :-

• The length of the lactus rectum hyperbola .

Solution :-

• The general equations for hyperbola is ,

$\frac{ {y}^{2} }{ {a}^{2} } - \frac{ {x}^{2} }{ {b}^{2} } = 1$

• Here dividing both LHS and RHS by 144 .
• we get that,

• $\frac{16 {y}^{2} }{?} - \frac{9 {x}^{2} }{144} = \frac{144}{144}$
• $\frac{ {y}^{2} }{9} - \frac{ {x}^{2} }{16} = 1$
• Here we know the formula to write the length of rectum hyperbola.

• That is ,

$length \: of \: LR = \frac{2 {b}^{2} }{a}$

• Comparing for general equation we get that,

• $length \: of \: LR = \frac{2 \times 16}{3} = \frac{32}{3}$

Therefore,

• The length of the latus rectum hyperbola is 32/3 units.

Hope it helps u mate .

Thank you .