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Find an equation of the circle with center at origin and radius ^@4^@.
Answer:
^@x^2 + y^2 = 16^@
- The equation of a circle with center at ^@(a, b)^@ and radius ^@r^@ is given by
^@(x - a)^2 + (y - b)^2 = r^2^@ - Given:
Center of the circle is at center ^@i.e(0,0)^@
Radius of the circle ^@ = 4^@
^@\implies a = 0, b = 0, ^@ and ^@r = 4 ^@ - Therefore, the equation of the circle is given by
^@(x - 0)^2 + (y - 0)^2 = 4^2 \\ \implies x^2 + y^2 = 16^@
Hence, the required equation is ^@x^2 + y^2 = 16^@.
