Differentiate the circle equation to find the slope at any given point.
x^2 + y^2 -6x + 4y -7 = 0
2x + 2y(dy/dx) - 6 + 4dy/dx =0
2x - 6 + (2y + 4) dy/dx =0
dy/dx = (6 - 2x) / (2y + +4)
At the point ( 1,2)
dy/dx = (6 - 2(1)) / (2(2) + 4)
dy/dx = 3 / 8 The slope /gradient of the tangent line.
At the point ( 1,2)
y - 2 = (3/8)(x - 1)
y - 2 = 3x/8 - 3/8
y = 3x/8 + 13/8
or
8y = 3x + 13
or
8y - 3x = 13
or
8y - 3x - 13 = 0
8
The tangent line equation touching the given circle works out as 2y = x+3 or as x-2y+3 = 0 in its general form
If the tangent circles are outside of one another, then neither passes through the center of the other. If one circle is within the other, then the inner tangent circle might contain the center point of the larger circle. There will be infinitely many inner tangent circles that do not.
The tangent line only touches the outside of a circle at one given point. So an outside line perpendicular to the circle's diameter at 90 degrees should do.
The diameter of a circle passes through the center of a circle at its center point
The radius-tangent theorem is math involving a circle. The radius-tangent theorem states that a line is tangent to a circle if it is perpendicular to the radius of a circle.
Infinite lines because a circle has infinite lines of symmetry.
a diameter
Circle equation: x^2 +y^2 -8x -16y -209 = 0 Completing the squares: (x-4)^2 +(y-8)^2 = 289 Centre of circle: (4, 8) Radius of circle 17 Slope of radius: 0 Perpendicular tangent slope: 0 Tangent point of contact: (21, 8) Tangent equation: x = 21 passing through (21, 0)
Circle passing through coordinate: (0, 0) Circle equation: x^2 +6 +y^2 -10 = 0 Completing the squares: (x+3)^2 +(y-5)^2 = 34 Centre of circle: (-3, 5) Slope of radius: -5/3 Slope of tangent: 3/5 Tangent equation: y-0 = 3/5(x-0) => y = 3/5x
Neither secant nor tangent pass through the center of a circle. A secant passes through one point on the circle and the tangent passes through two points on a circle.
Neither secant nor tangent pass through the center of a circle. A secant passes through one point on the circle and the tangent passes through two points on a circle.
Circle equation: x^2 +y^2 -8x -16y -209 Completing the squares: (x-4)^2 +(y-8)^2 = 289 Centre of circle: (4, 8) Radius: 17 Slope of radius: 0 Tangent equation line: x = 21 passing through (21, 0)
x2 + y2 = 49
A line joining the centres of two tangent circles also passes through the point of tangency.
the tangent will never go through the center of a cirlce. The tangent is, by definition, a line that only intersects the circle at one point. If you look down a pencil along its long axis, so that it appears to be a circle, and place your finger on top of and perpendicular to the pencil, your finger is now tangent to the circle you see.
Equation of the circle: (x-3)^2 +( y+13)^2 = 169
A tangent to a circle is a line which touches the circle once. That is, it does not pass through the circle, which would mean intersecting it twice. A way to form a tangent is draw any line from the centre point of a circle to its edge. A line on the edge perpendicular (at 90 degrees to) this line will be a tangent.
Circle equation: x^2 +y^2 +6x -10y = 0 Completing the squares: (x +3)^2 +(y -5)^2 = 34 Center of circle: (-3, 5) Point of contact: (0, 0) Slope of radius: -5/3 Slope of tangent line: 3/5 Tangent line equation: y = 0.6x