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Q: What is if two lines lies in the same plane and have more then one point in common?

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A point - unless the line lies within the plane, or is parallel to it.

co-planar

A single point lies in an infinite number of planes.

If you mean the point of (-1, 6) then it lies in the 2nd quadrant on the Cartesian plane

Nothing particularly. Just an infinite number of miscellaneous points in the plane.

You first look at each axes

A line that does not lie within a plane and intersects the plane does so at one point.A line that lies within a plane intersects the plane at all points.

A conic section is the intersection of a plane and a cone.The circle is a conic section where the plane is perpendicular to the axis of the cone. The special case of a point is where the vertex of the cone lies on the plane.The ellipse is a conic section where the plane is not perpendicular to the axis, but its angle is less than one of the nappes. The special case of a point is where the vertex of the cone lies on the plane.The parabola is a conic section where the plane is parallel to one of the nappes. The special case of two intersecting lines is where the vertex of the cone lies on the plane.The hyperbole is a conic section where the angle of the plane is greater than on of the nappes. There are two sides to the hyperbole. The special case of two lines intersecting is where the vertex of the cone lies on the plane.For more information, please see the Related Link below.

it always lies in that plane

You name it !No solid lies in a plane.

It has 2 lines of symmetry

Two lines that coincide look and act exactly like a single line. If you have one straight line, there are an infinite number of planes in which it lies.

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