the formula of algebra intersection

Statement :- Let a 1 x+b 1 y+c 1 =0 and a 2 x+b 2 y+c 2 =0 be two intersecting lines. Then (a 1 x+b 1 y+c 1 )+k(a 2 x+b 2 y+c 2 )=0 represents the family of straight lines passing through the intersection of given lines. Proof :- The equation (a 1 x+b 1 y+c 1 )+k(a 2 x+b..

The graph of a linear equation ax+by = c is a straight line. Two distinct lines always intersect at exactly one point unless they are parallel (have the same slope..

Pair of straight lines is a family of lines through the point of intersection of two lines.There are different theorems to support the features and proofs for the existence of pair of straight line..

There are chances that the plane passes through the apex of the cone. The intersection in this place can be a straight line (when the plane is tangential to the surface of the cone). A point (when the angle between the plane and the axis of the cone is larger than tangential); or a pair ..

- A hyperbola is the set of all points in the plane, the difference of whose distances from two fixed distinct points is a given positive constant that is less than the distance between the fixed points. The two fixed points are called the foci and the midpoint of the line segment joining foci is c..

- Circles, ellipses, parabolas, and hyperbolas are called conic sections because they can be obtained as a intersection of a plane with a double- napped circular cone. If the plane passes through vertex of the double-napped cone, then the intersection is a point, a pair of strai..

Rectangular axes - The position of a point in a plane is fixed by selecting two axes of reference which are formed by combining two number lines at right angles so that their zeros coincide. The horizontal number line is called x-axis and the vertical number line is called y-axis. The point of ..

Question: Use a graph paper for this question. Draw the graphs of 2x-y-1 = 0 and 2x + y = 9 on the same axes. Use 2cm = 1unit on both the axes and plot only three points per line. Write down the co-ordinates of the point of intersection of the two lines. Answer: 2x - y - 1 = 0..

Question: Draw the graphs of 6y=5x+10; 5x-y-15=0. Also find the coordinates of the point of intersection and area of the triangle between the lines and x-axis. Answer: 6y=5x+10 5x-y-15=0 5x-15=y x=0, y=-15 x=1, y=-10 x=2, y=-5 x=3, y=0..

A half-plane in the x-y plane is called a closed half-plane if the points on the line separating the half-planes are also included in the half-plane. A half-plane in the x-y plane is called a closed half-plane if the points on the line separating the half-planes are also included in the half-p..