Answer:
Option 4: x^2+y^2 = 52
Step-by-step explanation:
Given
Centre at origin
Point on circle = (-4, -6)
The distance between origin and point on circle will be the radius of the circle
So,
[tex]r = \sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}\\r= \sqrt{(-4-0)^2+(-6-0)^2} \\r = \sqrt{(-4)^2+(-6)^2}\\r = \sqrt{16+36} \\r = \sqrt{52}[/tex]
As the center is at origin the standard equation will be:
[tex]x^2+y^2 = r^2\\[/tex]
Putting the value of r
[tex]x^2+y^2 = (\sqrt{52})^2\\x^2+y^2 = 52[/tex]
Hence, last option i.e. Option 4 is correct ..
