Question
Analyze this conic section to answer the questions below: 6x^2 - 25y^2 - 224x - 384 = 0 What type of conic section is the equation? Circle Ellipse Parabola Hyperbola Where is the center of this conic section? Select the correct choice below and fill any answer become in your choice. (Type an ordered pair) The answer in undefined. What are the values of a and b for this conic section? Select the correct choice below and fill in any answer become in your choice a = and b = The answer is undefined. Determine the vertex or vertices for this conic section. This conic section has a vertex at(5, 4) This conic section has verties at. (B, O) and [4, 0]
Explanation / Answer
Rewriting 16x^2+25y^2-224x +384=0
16x^2+25y62-224x=-384
16(x^2-14x) +25y^2=-384
dividing by 16
(x^2 -14x) +25/16y^2=-24
Divide by 25
1/25(x^2-14x) +1/16y^2 =-24/25
1/25(x^2 -14x +49) +1/16y^2=-24/25 +49/25
1/25(x-7)^2 +1/16y^2=1
(x-7)^2/5^2 +(y-0)^2/4^2=1
1It is ellipse with
2.(h,k)=(7,0)
3.semi axis a= 5 b= 4