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# Pair of straight lines, Math Assignment Help

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Geometry Mathematics - Pair of straight lines, Math

**Pair of straight lines**

1. (i) The equation ax^{2} + 2hxy + by2 =0 represents a pair of straight

lines passing through the origin.

(ii) Let the lines represented by ax^{2} + 2hxy + by^{2} = 0 be y- m_{1}x = 0 and y - m_{2}x = 0, then

(iii) If a be the angle between the lines represented by ax^{2} + 2hxy + by^{2} = 0, then

tan q = ±

Hence,

(a) If h^{2} - ab > 0 then the lines represented by ax^{2} + 2hxy + by^{2} = 0 will be real and distinct.

(b) If h^{2} - ab = 0, then the lines are real and coincident.

(c) If h^{2} < ab, then the lines are imaginary and distinct.

(d) If a + b = 0, then the lines are perpendicular.

2. The equations of the bisectors of the angles between the lines represented by ax^{2} + 2hxy + by^{2} = 0 is given by

These bisectors lines will pass through origin also.

3. The equations of the lines passing through the origin and perpendicular to the lines represented by the equation

ax^{2} + 2hxy + by^{2} = 0 is bx^{2} - 2hxy + ay^{2} = 0

4. General equation of second degree in x, y is

ax^{2} + 2hxy + by^{2} + 2gx + 2fx + c = 0

This equation represents two straight lines, if

Δ = abc + 2fgh - af^{2} - bg^{2} - ch^{2} = 0

And point of intersection of these lines is given by

5. The angle between the two straight lines represented by (i) is given by

Hence,

(i) The lines are perpendicular, if a + b = 0

(ii) The lines are parallel, if h^{2} = ab

and af^{2} = bg^{2} or

(iii) The lines are coincident, if g^{2} = ac

6. The equation of the lines parallel to the lines represented by (i) equation and passing through origin is ax^{2} + 2hxy + by^{2} = 0.

7. The equation of the bisectors of the angles between the lines represented by (i) equation is

Where X = x - a and Y = g - ß and (a, ß) is point of intersection of the lines. Hence the equation of bisectors will be

8. The equation of the lines which joins origin to the point of intersection of the line x + my + n = 0 and curve ax^{2} + 2hxy + by^{2} + 2gx + 2fy + c = 0 can be obtained by making the curve homogeneous with the help of line x + my + n = 0, which is

ax^{2} + 2hxy + by^{2} + 2(gx + fy)

9. If ax^{2} + 2hxy + by^{2} + 2gX + 2fy + c = 0 represents a pair or parallel straight lines, then the distance between them is given by

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**Pair of straight lines**

^{2}+ 2hxy + by2 =0 represents a pair of straight

^{2}+ 2hxy + by

^{2}= 0 be y- m

_{1}x = 0 and y - m

_{2}x = 0, then

^{2}+ 2hxy + by

^{2}= 0, then

^{2}- ab > 0 then the lines represented by ax

^{2}+ 2hxy + by

^{2}= 0 will be real and distinct.

^{2}- ab = 0, then the lines are real and coincident.

^{2}< ab, then the lines are imaginary and distinct.

^{2}+ 2hxy + by

^{2}= 0 is given by

^{2}+ 2hxy + by

^{2}= 0 is bx

^{2}- 2hxy + ay

^{2}= 0

^{2}+ 2hxy + by

^{2}+ 2gx + 2fx + c = 0

^{2}- bg

^{2}- ch

^{2}= 0

^{2}= ab

^{2}= bg

^{2}or

^{2}= ac

^{2}+ 2hxy + by

^{2}= 0.

^{2}+ 2hxy + by

^{2}+ 2gx + 2fy + c = 0 can be obtained by making the curve homogeneous with the help of line x + my + n = 0, which is

^{2}+ 2hxy + by

^{2}+ 2(gx + fy)

^{2}+ 2hxy + by

^{2}+ 2gX + 2fy + c = 0 represents a pair or parallel straight lines, then the distance between them is given by

**Live Math Experts: Help with pair of straight lines Assignments - Homework**

**Math Online Tutoring**:

**Pairs of straight lines - Co -Ordinate Geometry**