<em>Answer:</em>
<em>The given equation is ellipse.</em>
<em>Step-by-step explanation:</em>
<em>Given : - </em>
<em>x² + 4y² + 2x - 24y + 33 = 0</em>
<em />
<em>Conic section formula, in the general form, could be written like this -</em>
<em>ax² + cy² +dx + ey + f = 0</em>
<em />
<em>The apply the following conditions to identify the equation.</em>
<em>If a = c, It is a circle.</em>
<em>If a x c = 0, It is a parabola.</em>
<em>If a x c > 0, It is a ellipse .</em>
<em>If a x c < 0,It is a hyperbola.</em>
<em />
<em>In this case:</em>
<em>a = 1;c = 4</em>
<em>1 x 4 = 4 > 0, then the</em><em> given equation is ellipse.</em>
