How can I write this Second Order Cone in a DCP form?

I am trying to solve an optimization problem and the constraint is in this form:

x’x <= t^2 + c^2;

x is a vector variable and t is a scalar variable and t>0 and c is a constant.

This shows a convex set since it is a part of a second order convex cone.
How can I write it in DCP form? Because it is Convex <= Convex form which CVX doesn’t accept it.


“It is a part of a second order convex cone.” What does that mean? That’s certainly not a valid proof of convexity. Indeed, this is not in fact convex.

Thanks for your response. Yes, It is actually nonconvex!