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The center of the circle is at (0, 0) and its radius is the square root of 1 which is 1

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What does length plus length plus width plus width equals?

it equals LxL+WxW


The equation of the inner circle is x2 plus y2 equals 4 the radius of the outer circle is four times the radius of the inner circle write the equation of the outer circle?

The inner circle is x2 + y2 = 4. The radius of the inner circle is the square root of 4, which is 2. To find the radius of the outer circle, multiply 2 times 4. The radius of the outer circle is 8. Square 8 (82 or 8 x 8) to find the number to put into the equation of the outer circle. This is 64. The equation for the outer circle is x2 + y2 = 64.


What is the length of the tangent line from the point 0 0 to a point where it touches the circle x2 plus y2 plus 4x -6y plus 10 equals 0 on the Cartesian plane?

Equation of the circle: x^2 +y^2 +4x -6y +10 = 0 Completing the squares: (x+2)^2 +(y-3)^2 = 3 Radius of the circle: square root of 3 Center of circle: (-2, 3) Distance from (0, 0) to (-2, 5) = sq rt of 13 which is the hypotenuse of right triangle. Using Pythagoras' theorem : distance squared - radius squared = 10 Therefore length of tangent line is the square root of 10 Note that the tangent of a circle meets its radius at right angles.


What is the center and radius of the circle x2 plus y2 -10x plus 6y -15 equals 0?

Equation of circle: x^2 +y^2 -10x +6y -15 = 0 Completing the squares: (x-5)^2 +(y+3)^2 = 49 square units Therefore center of circle is at (5, -3) and its radius is 7 units


What is the length of the tangent line from the point 9 0 to a point where it touches the circle of x2 plus 8x plus y2 -9 equals 0?

Equation of circle: x^2 +8x +y^2 -9 = 0 Completing the square: (x+4)^2 +y^2 = 25 Radius of circle: 5 Center of circle: (-4, 0) Distance from (9, 0) to (-4, 0) is 13 which is the hypotenuse of a right angle triangle Using Pythagoras' theorem: 13^2 -5^2 = 144 and its square root is 12 Therefore length of tangent line is: 12 units Note that a tangent line always meets the radius of a circle at right angles.