1, intersection
A hyperbola intersects a straight line at a certain point. At this time, the intersection of the focus of the hyperbola and the straight line is on the X axis. You can solve the coordinates of the intersection point by algebraic method.
Step 2 contact
The hyperbola is tangent to the straight line at a certain point, and the intersection of hyperbola and straight line is on the X axis. The tangent coordinates can be solved by algebraic method.
Step 3 separate
Hyperbola and straight line are separated at a certain point, and the intersection of hyperbola and straight line is on the X axis. You can solve the coordinates of the distance by algebraic method.
Brief introduction of hyperbola and straight line
1, hyperbola
Hyperbola is a conic curve, which is defined as the intersection of two halves of a plane and a right-angled conical surface. It can also be defined as the trajectory of a point whose distance difference from two fixed points (called focus) is constant.
The geometric properties of hyperbola can be divided into two categories. Position relationship: the center is the midpoint of two focal points and two vertices; The focus is on the real axis; The real axis is perpendicular to the imaginary axis; A hyperbola has two asymptotes passing through the center; The directrix is perpendicular to the real axis. The distance between two directrix is the focal length (focal length parameter).
Mathematically, hyperbola (multiple hyperbola or hyperbola) is a smooth curve on a plane, which is defined by the equation of its geometric characteristics or the combination of its solutions. A hyperbola has two parts, called connected components or branches, which are mirror images of each other, similar to two infinite bows. Hyperbola is one of the three conic curves formed by the intersection of plane and double cone.
Step 2: Straight line
A straight line is composed of countless points, which is a part of a surface and then constitutes a body. It has no end points, can extend to both ends indefinitely, and its length cannot be measured. There is only one straight line between two non-overlapping points on the plane, that is, two non-overlapping points determine a straight line. On the sphere, countless similar straight lines can be made after two points.
In Euclidean geometry, straight line is regarded as one of the most basic geometric elements, and other basic elements include points, faces and so on. The properties and axioms of straight lines are widely used to prove and deduce various geometric theorems and formulas.