In this article, we shall study to write vector and cartesian equation of a line in Space. Theorem – 1 (Vector Equation of Line in Space): The vector equation of a straight line passing through a fixed point with position vector a and parallel to a given vector b is r = a + λ b. Where […]
In this article, we shall study to find the distance between two points using the distance formula when the coordinates of the two points are given. Example 01: Find the distance between the following pairs of points : (2, 3), (4, 1) Let A(2, 3) ≡ (x1, y1) and B(4, 1) ≡ (x2, y2) be […]
Science > Mathematics > Pair of Straight Lines > To Find the Condition When Relation Between Slopes is Given In this article, we shall discuss problems to find the condition when the relation between slopes of lines represented by a joint equation is given. Example – 18: If the slope of one of the lines […]
Science > Mathematics > Pair of Straight Lines > To Find Value of Constant When Relation Between Slopes is Given In this article, we shall study to solve problems to find the value of constant or to prove the given relation when the relation between slopes of the line represented by the joint equation is […]
A circle is defined as the locus of all the points in a plane, which are at a fixed distance from a fixed point. The fixed point is called the centre of the circle and the fixed distance is called the radius of the circle. The radius of a circle is denoted by the letter […]
Science > Mathematics > Pair of Straight Lines > Condition That Line is Represented by Homogeneous Equation In this article, we shall study problems to find the condition when one of the lines represented by a homogeneous equation is given. ALGORITHM : Write the auxiliary equation of joint equation. Find the slope of given line […]
Science > Mathematics > Pair of Straight Lines > Use of Auxiliary Equation of Pair of Lines In this article, we shall study the use of the auxiliary equation of par of lines to find the required condition. Algorithm: Write the auxiliary equation of the joint equation. Find the slope of given line m. Substitute […]
Science > Mathematics > Pair of Straight Lines > Joint Equation of Pair of Lines Perpendicular To Another Pair of Lines In this article, we shall study to find a joint equation of lines perpendicular to another pair of lines. Note: If m1 and m2 are the slopes of the two lines represented by joint […]
Science > Mathematics > Pair of Straight Lines > Nature of Lines Represented by Joint Equation In this article, we shall study to predict the nature of lines using the joint equations of lines. Notes: If ax2 + 2hxy + by2= 0 is a joint equation of lines then the lines represented by joint equation […]
Science > Mathematics > Pair of Straight Lines > Separate Equations of Lines (Auxillary Equation Method) In this article, we shall study to find separate equations of lines from a combined or joint equation of pair of lines by auxiliary equation method. Algorithm: Check if lines exist. use the same method used in the case […]