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Find the separate equation of the line represented by the following equation:
3y2 + 7xy = 0
Concept: Combined Equation of a Pair Lines
Find k, the slope of one of the lines given by kx2 + 4xy – y2 = 0 exceeds the slope of the other by 8.
Concept: Homogeneous Equation of Degree Two
If one of the lines given by ax2 + 2hxy + by2 = 0 bisects an angle between the coordinate axes, then show that (a + b)2 = 4h2.
Concept: Homogeneous Equation of Degree Two
Find the coordinates of the points of intersection of the lines represented by x2 − y2 − 2x + 1 = 0
Concept: General Second Degree Equation
The area of triangle formed by the lines x2 + 4xy + y2 = 0 and x - y - 4 = 0 is ______.
Concept: Combined Equation of a Pair Lines
Find the joint equation of the line passing through the origin having slopes 2 and 3.
Concept: Combined Equation of a Pair Lines
Show that the difference between the slopes of the lines given by (tan2θ + cos2θ)x2 − 2xy tan θ + (sin2θ)y2 = 0 is two.
Concept: Angle between Lines Represented by ax² + 2hxy + by² = 0
The combined equation of the lines through origin and perpendicular to the pair of lines 3x2 + 4xy − 5y2 = 0 is ______
Concept: Combined Equation of a Pair Lines
Find the value of h, if the measure of the angle between the lines 3x2 + 2hxy + 2y2 = 0 is 45°.
Concept: Angle between Lines Represented by ax² + 2hxy + by² = 0
Show that the combined equation of pair of lines passing through the origin is a homogeneous equation of degree 2 in x and y. Hence find the combined equation of the lines 2x + 3y = 0 and x − 2y = 0
Concept: Combined Equation of a Pair Lines
If θ is the acute angle between the lines given by ax2 + 2hxy + by2 = 0 then prove that tan θ = `|(2sqrt("h"^2) - "ab")/("a" + "b")|`. Hence find acute angle between the lines 2x2 + 7xy + 3y2 = 0
Concept: Angle between Lines Represented by ax² + 2hxy + by² = 0
If the angle between the lines represented by ax2 + 2hxy + by2 = 0 is equal to the angle between the lines 2x2 − 5xy + 3y2 = 0, then show that 100(h2 − ab) = (a + b)2
Concept: Angle between Lines Represented by ax² + 2hxy + by² = 0
Equation of line passing through the points (0, 0, 0) and (2, 1, –3) is ______.
Concept: General Second Degree Equation
Write the separate equations of lines represented by the equation 5x2 – 9y2 = 0
Concept: Combined Equation of a Pair Lines
Find the value of k. if 2x + y = 0 is one of the lines represented by 3x2 + kxy + 2y2 = 0
Concept: Homogeneous Equation of Degree Two
Write the joint equation of co-ordinate axes.
Concept: Combined Equation of a Pair Lines
If ax2 + 2hxy + by2 = 0 represents a pair of lines and h2 = ab ≠ 0 then find the ratio of their slopes.
Concept: Angle between Lines Represented by ax² + 2hxy + by² = 0
If θ is the acute angle between the lines represented by ax2 + 2hxy + by2 = 0 then prove that tan θ = `|(2sqrt(h^2 - ab))/(a + b)|`
Concept: Angle between Lines Represented by ax² + 2hxy + by² = 0
Prove that the acute angle θ between the lines represented by the equation ax2 + 2hxy+ by2 = 0 is tanθ = `|(2sqrt(h^2 - ab))/(a + b)|` Hence find the condition that the lines are coincident.
Concept: Angle between Lines Represented by ax² + 2hxy + by² = 0
If `bar c = 3bara- 2bar b ` Prove that `[bar a bar b barc]=0`
Concept: Scalar Triple Product
