Respuesta :
Answer:
The conic section that represents the equation 3x + 4y = 12 is a line.
3x + 4y = 12 represents the equation of the line from the given options of the conic section circle ,ellipse, parabola, hyperbola, line.
What is conic section ?
" Conic section defined as the curve which is obtained when the plane is cut out from the cone."
According to the question,
Circle : Equation of the circle given by [tex](x-h)^{2} + (y-k)^{2} =r^{2}[/tex]
Conic section circle is not the correct answer.
Ellipse : Equation of the ellipse given by [tex]\frac{x^{2} }{a^{2}} + \frac{y^{2} }{b^{2}}=1[/tex]
Conic section ellipse is not the correct answer.
Parabola : Equation of the Parabola given by [tex]y^{2} = 4ax[/tex]
Conic section parabola is not the correct answer.
Hyperbola: Equation of the Hyperbola given by [tex]\frac{x^{2} }{a^{2}} - \frac{y^{2} }{b^{2}}=1[/tex]
Conic section hyperbola is not the correct answer.
Line : Equation of the line given by [tex]Ax + By + C =0[/tex]
3x + 4y = 12 represents [tex]Ax + By + C =0[/tex] .
Hence, 3x + 4y = 12 represents the equation of the line.
Learn more about conic section here
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