Respuesta :
The conic section which is represented by the provide equation is the equation of ellipse and represent ellipse conic section.
How to identify the type of conic section from an equation?
To of identify the type of conic section from an equation whether it is circle, or ellipse a let suppose the equation as,
[tex]Ax^2+By^2+Cx+Dy+E=0[/tex]
In this equation, if,
[tex]A\neq B[/tex]
Then it is the equation of circle.
If In this equation,
[tex]A\neq B[/tex]
But both A and B has same sign (either positive or negative) then it is the equation of ellipse.
The given equation in the problem is,
[tex]3x^2 - 7x+ 8y^2 - 2y+ 1 = 0[/tex]
Here, in the equation,
[tex]A=3\\B=8[/tex]
The A is not equal to B but the sign of both are positive. Hence this equation is the equation of ellipse.
Hence, the conic section which is represented by the provide equation is the equation of ellipse and represent ellipse conic section.
Learn more about the conic section here;
https://brainly.com/question/8320698
