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What is the centre and radius of the circle whose equation is 100x2 plus 100y2 -120x plus 100y -39 equals 0 on the Cartesian plane?
A circle with centre (X, Y) and radius r has an equation of the form:
(x - X)² + (y - Y)² = r²
Dividing through by 100, completing the square and rearranging gives:
100x² + 100y² - 120x + 100y - 39 = 0
→ x² - (6/5)x + y² + y - 39/100 = 0
→ (x - (6/10))² - (6/10)² +(y + 1/2)² - (1/2)² - 39/100 = 0
→ (x - 3/5)² - 36/100 + (y + 1/2)² - 1/4 - 39/100 = 0
→ (x - 3/5)² + (y + 1/2)² - 1/4 - 75/100 = 0
→ (x - 3/5)² + (y + 1/2)² = 1/4 + 3/4
→ (x - 3/5)² + (y - (-1/2))² = 1 = 1²
→ Circle has centre (3/5, -1/2) = (0.6, -0.5) and radius 1.
What else can I help you with?
How can you tell if the graph of an equation in the form ax2 plus by2 equals c is a circle or an ellipse?
If a = b then it is a circle; otherwise it is an ellipse.
What is the center of a circle for the equation 3x2 plus 3y2 - 30x plus 27 equals 0?
56
What is the answer to x squared plus y squared equals 25?
xx^(2) + y^(2) = 25 => x^(2) + y^(2) = 5^(2) This is the circle equation, in Cartesian Co-ordinates. It is also the Pythagorean Eq'n.
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 tangent line equation that touches the circle of x squared plus y squared -6x plus 4y -7 equals 0 at the point of 1 2 on the Cartesian plane showing work?
The line tangent to a circle is perpendicular to the radius from the centre of the circle to the point of contact. A circle with centre (X, Y) and radius r has equation: (x - X)² + (y - Y)² = r² Re-arranging x² + y² -6x + 4y -7 = 0 into this form allows us to find the centre of the circle. This requires completing the square in both x and y: x² + y² - 6x + 4y - 7 = 0 → x² -6x + 9 - 9 + y² + 4y + 4 - 4 - 7 = 0 → (x - 3)² - 9 + (y + 2)² - 4 - 7 = 0 → (x - 3)² + (y + 2)² - 20 = 0 → (x - 3)² + (y + 2)² = 20 → the centre of the circle is at (3, -2). The slope of the radius between this centre and the point of touch at (1, 2) is given by: m = change_in_y / change_in_x = (2 - -2)/(1 - 3) = 4/-2 = -2 The slope m' of a line perpendicular to a line of slope m is such that mm' = -1 → m' = -1/m → the slope of the tangent m' is m' = -1/-2 = 1/2 The equation of a line through point (x0, y0) with slope m is given by: y - y0 = m(x - x0) Thus the equation of the tangent (with slope 1/2) to the circle at (1, 2) is: y - 2 = ½(x - 1) → 2y - 4 = x - 1 → 2y = x + 3 → 2y - x = 3 (or y = x/2 + 1.5)
What is the radius for a circle with the equation x2 plus y2 equals 9?
Equation of a circle centre the origin is: x2 + y2 = radius2 ⇒ radius = √9 = 3.
What the radius for a circle with the equation x2 plus y2 equals 25?
5. A circle with centre (0,0) has equation: x2 + y2 = radius2 With: x2 + y2 = 25 = 52 The radius is 5.
What is the radius equation inside the circle x squared plus y squared -8x plus 4y equals 30 that meets the tangent line y equals x plus 4 on the Cartesian plane showing work?
Circle equation: x^2 +y^2 -8x +4y = 30 Tangent line equation: y = x+4 Centre of circle: (4, -2) Slope of radius: -1 Radius equation: y--2 = -1(x-4) => y = -x+2 Note that this proves that tangent of a circle is always at right angles to its radius
What is the center and the radius of the circle with this equation x2 plus y2 equals 121?
Centre = (0,0), the origin; radius = 11
What is the radius of the circle with the equation x² plus y² equals 36?
A circle centre (0, 0) and radius r has equation x² + y² = r² The circle x² + y² = 36 has: r² = 36 → radius = 6
What is the centre and radius of a circle embeded on the Cartesian plane whose equation is x squared plus y squared -4x -2y -4 equals 0 showing key aspects of work?
Note that: (x-a)2+(y-b)2 = radius2 whereas a and b are the coordinates of the circle's centre Equation: x2+y2-4x-2y-4 = 0 Completing the squares: (x-2)2+(y-1)2 = 9 Therefore: centre = (2, 1) and radius = 3
How do you solve x squared plus y squared equals 13?
The equation describes a circle with its centre at the origin and radius = √13. Each and every point on that circle is a solution.
Where is the center of the circle given by the equation x plus 52 plus y-32 equals 56?
There need to be squares in there for x and y - I think you're asking for the centre of the circle with equation: (x + 5)2 + (y - 3)2 = 56 in which case the centre is (-5, 3) A circle with centre (xo, yo) and radius r has equation of the form: (x - xo)2 + (y - yo)2 = r2
What is the tangent equation that touches the circle x2 -y2 -8x -16y -209 equals 0 at the point of 21 and 8 on the Cartesian plane?
Point of contact: (21, 8) Equation of circle: x^2 -y^2 -8x -16y -209 = 0 Completing the squares: (x-4)^2 +(y-8)^2 = 289 Centre of circle: (4, 8) and its radius is 17 Slope of radius: 0 Slope of tangent: 0 Tangent equation of the circle: x = 21 meaning that the tangent line is parallel to the y axis and that the radius is parallel to the x axis.
Where is the center of the circle given by the equation x plus 5 squared plus y minus 3 squared equals 25?
The centre is (-5, 3)
What is x squared plus 25 times y squared equals 50?
It is the Cartesian equation of an ellipse.
What is the cartesian equation for the vector function rt equals 4costi-4sintj?
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