Question

Identify the conic with equation 16y^2-x^2+x-4y-9+0CircleParabolaHyperbolaEllipseThis is an assgement I don’t understand I need an explanation please

Answer 1

we have the equation

`16y^2-x^2+x-4y-9=0`

step 1

Group similar terms and move the constant term to the right side

`(16y^2-4y)+(-x^2+x)=9`

step 2

Factor 16 in the first term and factor -1 in the second term

`16(y^2-(y)/(4))-(x^2-x)=9`

step 2

Complete the square twice

`16(y^2-(y)/(4)+(1)/(64)-(1)/(64))-(x^2-x+(1)/(4)-(1)/(4))=9`
`16(y^2-y\/4+1\/64)-(x^2-x+1\/4)=9+(1)/(4)-(1)/(4)`

step 3

Rewrite as perfect squares

`16(y-(1)/(8))^2-(x-(1)/(2))^2=9`

step 4

Divide both sides by 9

`(16(y-1\/8)^2)/(9)-((x-1\/2)^2)/(9)=1`

therefore

The answer is Hyperbola