Answer:
A
Step-by-step explanation:
Use formulas:
[tex]r=\sqrt{x^2+y^2},[/tex]
[tex]\cos \theta=\dfrac{x}{\sqrt{x^2+y^2}}.[/tex]
Substitute them into the equation [tex]r=-14\cos \theta:[/tex]
[tex]\sqrt{x^2+y^2}=-14\cdot \dfrac{x}{\sqrt{x^2+y^2}}.[/tex]
Multiply this equation by [tex]\sqrt{x^2+y^2}:[/tex]
[tex]x^2+y^2=-14x.[/tex]
Now rewrite this equation as
[tex]x^2+14x+y^2=0,\\ \\x^2+14x+49-49+y^2=0,\\ \\(x+7)^2+y^2=49.[/tex]
This is the equation of the circle with center at point (-7,0) and radius r=7 (diameter 14).
