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Find the joint equation of the line: x + y − 3 = 0 and 2x + y − 1 = 0 - Mathematics and Statistics

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प्रश्न

Find the joint equation of the line:

x + y − 3 = 0 and 2x + y − 1 = 0

बेरीज
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उत्तर

Find the joint equation of the line x + y − 3 = 0 and 2x + y − 1 = 0

(x + y − 3)(2x + y − 1) = 0

∴ 2x2 + xy - x + 2xy + y2 − y − 6x − 3y + 3 = 0

∴ 2x2 + 3xy + y2 − 7x − 4y + 3 = 0

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पाठ 4: Pair of Straight Lines - Miscellaneous Exercise 4 [पृष्ठ १३०]

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बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
पाठ 4 Pair of Straight Lines
Miscellaneous Exercise 4 | Q 1.02 | पृष्ठ १३०

संबंधित प्रश्‍न

Find the combined equation of the following pair of lines:

2x + y = 0 and 3x − y = 0


Find the combined equation of the following pair of lines passing through point (2, 3) and parallel to the coordinate axes.


Find the combined equation of the following pair of lines:

Passing through (2, 3) and perpendicular to the lines 3x + 2y – 1 = 0 and x – 3y + 2 = 0.


Find the combined equation of the following pair of line passing through (−1, 2), one is parallel to x + 3y − 1 = 0 and other is perpendicular to 2x − 3y − 1 = 0


Find the separate equation of the line represented by the following equation:

5x2 – 9y2 = 0


Find the separate equation of the line represented by the following equation:

x2 + 2(cosec α)xy + y2 = 0


Find the separate equation of the line represented by the following equation:

x2 + 2xy tan α - y2 = 0


Find the combined equation of the pair of a line passing through the origin and perpendicular to the line represented by following equation:

5x2 - 8xy + 3y2 = 0 


Find the combined equation of the pair of a line passing through the origin and perpendicular to the line represented by the following equation:

xy + y2 = 0 


Choose correct alternatives:

Auxiliary equation of 2x2 + 3xy - 9y2 = 0 is


Choose correct alternatives:

If the equation 3x2 – 8xy + qy2 + 2x + 14y + p = 1 represents a pair of perpendicular lines, then the values of p and q are respectively ______.


Choose correct alternatives:

The combined equation of the coordinate axes is


Choose correct alternatives:

If distance between lines (x - 2y)2 + k(x - 2y) = 0 is 3 units, then k = ______.


Find the joint equation of the line passing through the origin having slopes 2 and 3.


Find the joint equation of the line passing through the point (3, 2), one of which is parallel to the line x - 2y = 2, and other is perpendicular to the line y = 3.


Show that the following equations represent a pair of line:

x2 - y2 = 0


Find the separate equation of the line represented by the following equation:

6x2 - 5xy - 6y2 = 0


Find the joint equation of the pair of a line through the origin and perpendicular to the lines given by

x2 + 4xy - 5y2 = 0


Find the joint equation of the pair of a line through the origin and perpendicular to the lines given by

x2 + xy - y2 = 0


Find k, if the sum of the slopes of the lines given by x2 + kxy − 3y2 = 0 is equal to their product.


Find k, if the slope of one of the lines given by 3x2 - 4xy + ky2 = 0 is 1.


Find k, if the slope of one of the lines given by 3x2 + 4xy + ky2 = 0 is three times the other.


Find k, if one of the lines given by 6x2 + kxy + y2 = 0 is 2x + y = 0.


Find the joint equation of the pair of lines through the origin and making an equilateral triangle with the line x = 3.


Find a if the sum of the slopes of lines represented by ax2 + 8xy + 5y2 = 0 is twice their product.


Show that the following equation represents a pair of line. Find the acute angle between them:

(x - 3)2 + (x - 3)(y - 4) - 2(y - 4)2 = 0


Show that the combined equation of the pair of lines passing through the origin and each making an angle α with the line x + y = 0 is x2 + 2(sec 2α)xy + y2 = 0


If the line x + 2 = 0 coincides with one of the lines represented by the equation x2 + 2xy + 4y + k = 0, then prove that k = - 4. 


Prove that the combined of the pair of lines passing through the origin and perpendicular to the lines ax2 + 2hxy + by2 = 0 is bx2 - 2hxy + ay2 = 0.


Find k if the slope of one of the lines given by 3x2 + 4xy + ky2 = 0 is three times the other.


Find the joint equation of the line passing through the origin and having slopes 1 + `sqrt3` and 1 - `sqrt3`


The combined equation of the lines through origin and perpendicular to the pair of lines 3x2 + 4xy − 5y2 = 0 is ______


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


The joint equation of pair of straight lines passing through origin and having slopes `(1 + sqrt2) and (1/(1 + sqrt2))` is ______.


The joint equation of the lines through the origin which forms two of the sides of the equilateral triangle having x = 2 as the third side is ______


The equation of line passing through the midpoint of the line joining the points (-1, 3, -2) and (-5, 3, -6) and equally inclined to the axes is ______.


The joint equation of pair of lines having slopes 2 and 5 and passing through the origin is ______.


Write the separate equations of lines represented by the equation 5x2 – 9y2 = 0


Write the joint equation of co-ordinate axes.


Find the combined equation of the pair of lines passing through the origin and perpendicular to the lines represented by 3x2 + 2xy – y2 = 0.


Find k, if one of the lines given by kx2 – 5xy – 3y2 = 0 is perpendicular to the line x – 2y + 3 = 0


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