Question

Lots of points. Show work and i will give you brainliest.

a telescope is built using a hyperbolic mirror modeled by the equation (x^2)/(400) + (y^2)/(144) = 1, and a parabolic mirror that opens downward. The parabola has the vertex (-1,-4) and shares a focus with the hyperbola. What are the coordinates of the focus they share?

Answer 1

The coordinates of the focus that parabola and hyperbola share is (-4 , -12) .

In the question ,

it is given that ,

the hyperbolic equation of the mirror is  (y-1)²/144 - (x+4)²/25 = 1

and given that the parabola opens down wards ,

the eccentricity of the hyperbola(e) = √(1 + 144/25)

= √(169/25)

= 13/5

we know that the focus of the hyperbola is = (-4 , 1 ± a*e )

= (-4 , 1 ± 5*(13/5))

= ( -4 , 1 ± 13 )

= (-4 , 14 )    and   (-4 , -12)

Since the parabola open down wards so , the focus will be  (-4 , -12) .

Therefore , The coordinates of the focus that parabola and hyperbola share is (-4 , -12) .

The given question is incomplete , the complete question  is

A telescope is built using a hyperbolic mirror modeled by the equation (y-1)²/144 - (x+4)²/25 = 1, and a parabolic mirror that opens downward. The parabola has the vertex (-1,-4) and shares a focus with the hyperbola. What are the coordinates of the focus they share ?

Learn more about Parabola here

https://brainly.com/question/10684698

#SPJ4