Question

find the equation of the hyperbola with center at the origin, length of conjugate axis 10 and one of the foci(-7,0)​

Answer 1

the equation of the hyperbola with center at the origin, length of conjugate axis 10 and one of the foci(-7,0)​ is   $\dfrac{x^2}{24} - \dfrac{y^2}{25} = 1$

• Given
• f(-7,0)
• ⇒ c = -7
• 2b = 10
• ⇒ b =5
• ∴ b^2 =25
• c^2 = a^2 + b^2
• (-7)^2 = a^2 + 5^2
• a^2 = 49 - 25 = 24
• ∴ a^2 = 24
• Now, the equation of hyperbola is,
• $\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1$
• $\dfrac{x^2}{24} - \dfrac{y^2}{25} = 1$

Answer 2

Answer:

The equation of parabola with given center at origin is $\dfrac{x^{2} }{ 24}$  - $\dfrac{y^{2} }{ 25}$  = 1

Step-by-step explanation:

Given as :

For hyperbola

The center at the origin

Length of conjugate axis = 10

co-ordinate of foci = ( - 7 , 0 )

i.e 2 b = 10

Or, b = $\dfrac{10}{2}$

Or, b = 5

or, b² = 25

Again

The distance between the two foci = 2 c

And c² = a² + b²

∵  co-ordinate of foci = ( $\pm$ c , 0 )

So, c = - 7

Or , (-7)² = a² + 5²

Or, 49  = a² + 25

or, a² = 49 - 25

Or, a² = 24

Now,

The standard equation of hyperbola =  $\dfrac{x^{2} }{a^{2} }$  - $\dfrac{y^{2} }{b^{2} }$  = 1

Substitute value of  a² = 24  , b² = 25 in hyperbolas standard equation

So, $\dfrac{x^{2} }{ 24}$  - $\dfrac{y^{2} }{ 25}$  = 1

Hence, The equation of parabola with given center at origin is $\dfrac{x^{2} }{ 24}$  - $\dfrac{y^{2} }{ 25}$  = 1 Answer