Which of the following is the correct definition of a circle found within a plane in terms of a center (h, k) and radius r?

Which statement is true about the curve defined by $x^2+y^2=49$?

Convert $x^2+y^2+\frac{1}{3}x-\frac{5}{2}y-1=0$ into standard form.

Decide whether $x^2+y^2+2x+4y+10=0$ represents a real circle. Explain your reasoning to justify.

Convert $2x^2+2y^2+8x-12y+6=0$ into standard form. What is the standard form, center, and radius of this circle?