In mathematics, the simultaneous problem of straight lines and conic curves is an important and interesting research field. Using Vieta theorem, we can solve these problems more conveniently. This paper will discuss in detail the method of establishing straight lines and conic curves at the same time and how to use Vieta theorem to solve them.
First of all, let's solve the simultaneous problem of straight line and conic curve. The simultaneous problem of straight line and conic curve mainly includes solving the coordinates of intersection points, judging the number and nature of intersection points and so on. When solving these problems, we can combine the equations of straight line and conic curve to get a set of equations. Then the coordinates of the intersection point are obtained by solving the equation.
Next, let's get to know Vieta's theorem. Vieta theorem is a theorem about the relationship between the roots and coefficients of quadratic function. It shows that the sum and product of two roots of general quadratic equation are equal to the sum and product of coefficient ratio respectively. That is, x1+x2 =-b/ax1* x2 = c/a, where a, b and c are the coefficients of the unary quadratic equation ax 2+bx+c = 0 respectively.
In the simultaneous problem of straight lines and conic curves, we can turn the equations of straight lines and conic curves into standard formulas or general formulas. Then, through Vieta theorem, the coordinates and properties of the intersection point are solved. It should be noted that in the process of solving, we need to use Vieta's theorem flexibly according to the form of the equation.
When a straight line intersects an ellipse, we can get a binary quadratic equation about X and Y through the simultaneous equation of the straight line and ellipse. Then Vieta theorem is used to solve the coordinates and properties of the intersection. When a straight line intersects a hyperbola, we can solve the coordinates and properties of the intersection point in a similar way.
The simultaneous problem of straight lines and conic curves is an interesting and important research field. Using Vieta theorem, we can solve these problems more conveniently. In practical application, it is necessary to flexibly apply Vieta's theorem according to the form of the equation to obtain the coordinates and properties of the intersection point.