Find the equation of a circle with a center at (0, -4) and a point on the circle is (6, 0).

Mathematics

1 answer:

EastWind [94]2 years ago

8 0

Answer:

$x^2 + ( y + 4)^2 = 52$

Step-by-step explanation:

Equation of circle with center (a , b) and radius, r is :

$(x -a)^2 + ( y -b)^2 = r^2$

Given : a = 0 , b = - 4

Step 1 : Find the radius.

Given ( 6 , 0 ) lies on the circle. Therefore the distance between the center (0 , - 4) of the circle and ( 6 , 0 ) gives the radius of the circle.

$r = \sqrt{( 0 - 6)^2 + ( -4 - 0)^2} \\\\$

$= \sqrt{ 36 + 16 } \\\\= \sqrt{52}$

Step 2 : Equation of circle.

$(x - 0)^2 + (y -( - 4))^2 = (\sqrt{52})^2\\\\x^2 + ( y+ 4)^2 = 52$

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