Question 1092186
<br>The conic is an ellipse, because it has x squared and y squared terms that have the same sign and different coefficients.<br>
Complete the square in both variables....<br>
{{{2x^2 + 5y^2 - 30y + 8x = a}}}
{{{2(x^2+4x)+5(y^2-6y) = a}}}
{{{2(x^2+4x+4)+5(y^2-6y+9) = a+2(4)+5(9)}}}
{{{2(x+2)^2+5(y-3)^2 = a+53}}}<br>
The graph will be an ellipse if a+53 is positive.
The graph will be a single point if a+53 is equal to 0.
The graph will have no points if a+53 is negative.<br>
So the graph will have at least one point if a+53 is greater than or equal to 0; i.e., if a is greater than or equal to -53.<br>
Answer in interval notation:  [-53, infinity)