Equation of circle: x^2 +y^2 -6x +4y +5 = 0
Completing the squares (x -3)^2 +(y +2)^2 = 8
Centre of circle: (3, -2)
Radius of circle: square root of 8
Points of contact are at: (1, 0) and (5, 0) where the radii touches the x axis
Slope of 1st tangent line: 1
Slope of 2nd tangent line: -1
Equation of 1st tangent: y -0 = 1(x -1) => y = x -1
Equation of 2nd tangent: y -0 = -1(x -5) => y = -x +5
No, only at one point, perpendicular to the radius
The answer will depend on where the points a, b and g are as well as where angle 1 is. Since there is no information provided for these, it is not possible to answer the question
Yes. A circle is defined as the set of all points in a plane equidistant from a given point (the center of the circle) - hence - all points of a circle must be co-planar by definition.
It is the centre of the circle
A chord line intersects a circle at two points of which the circle's diameter is its largest chord.
tangent
No. A tangent touches the circle at exactly one point. A line that intersects a circle at exactly two points is a secant.
Circle equation: x^2 +y^2 -6x +4y +5 = 0 Completing the squares: (x-3)^2 +(y+2)^2 = 8 Center of circle: (3, -2) Radius of circle: square root of 8 The radius of the circle will touch the points of (1, 0) and (5, 0) on the x axis The tangent slope at (1, 0) is 1 The tangent slope at (5, 0) is -1 Equations of the tangents are: y = x-1 and y = -x+5
1
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.
No, only at one point, perpendicular to the radius
Step I: Show that both points are outside the smaller circles. Possibly by showing that distance from each point to the centre of the circle is greater than its radius. Step 2: Show that the line between the two points touches the circle at exactly one point. This would be by simultaneous solution of the equations of the line and the circle.
Linear equations or inequalities describe points x y that lie on a circle.
A secant line touches a circle at two points. On the other hand a tangent line meets a circle at one point.
Tangent
Yes, it can as long as it is not the tangent line of the outermost circle. If it is tangent to any of the inner circles it will always cross the outer circles at two points--so it is their secant line--whereas the tangent of the outermost circle is secant to no circle because there are no more circles beyond that last one.