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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Choose correct alternatives: If slope of one of the lines ax2 + 2hxy + by2 = 0 is 5 times the slope of the other, then 5h2 = ______

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प्रश्न

Choose correct alternatives:

If slope of one of the lines ax2 + 2hxy + by2 = 0 is 5 times the slope of the other, then 5h2 = ______

पर्याय

  • ab

  • 2ab

  • 7ab

  • 9ab

MCQ
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उत्तर

If slope of one of the lines ax2 + 2hxy + by2 = 0 is 5 times the slope of the other, then 5h29ab.

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Notes

The answer in the textbook is incorrect.

  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 4: Pair of Straight Lines - Miscellaneous Exercise 4 [पृष्ठ १३०]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
पाठ 4 Pair of Straight Lines
Miscellaneous Exercise 4 | Q 1.13 | पृष्ठ १३०

संबंधित प्रश्‍न

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:

x2 - 4xy = 0 


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

`3"x"^2 - 2sqrt3"xy" - 3"y"^2 = 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 the following equation:

5x2 + 2xy - 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:

3x2 − 4xy = 0 


Choose correct alternatives:

If two lines ax2 + 2hxy + by2 = 0 make angles α and β with X-axis, then tan (α + β) = _____.


The area of triangle formed by the lines x2 + 4xy + y2 = 0 and x - y - 4 = 0 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:

x - y = 0 and x + y = 0


Find the joint equation of the line:

x + y − 3 = 0 and 2x + y − 1 = 0


Find the joint equation of the line passing through the origin and having inclinations 60° and 120°.


Find the joint equation of the line passing through (1, 2) and parallel to the coordinate axes


Find the joint equation of the line passing through (3, 2) and parallel to the lines x = 2 and y  = 3.


Find the joint equation of the line passing through the origin and perpendicular to the lines x + 2y = 19 and 3x + y = 18


Show that the following equations represents a pair of line:

4x2 + 4xy + y2 = 0


Show that the following equations represent a pair of line:

x2 + 7xy - 2y2 = 0


Show that the following equations represent a pair of line:

`"x"^2 - 2sqrt3"xy" - "y"^2 = 0`


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

2x2 + 2xy - y2 = 0


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

2x2 - 3xy - 9y2 = 0


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


Find k, if one of the lines given by 3x2 - kxy + 5y2 = 0 is perpendicular to the line 5x + 3y = 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 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 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 equation ax2 - y2 + 2y + c = 1 represents a pair of perpendicular lines, then find a and c.


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


The combined equation of the two lines passing through the origin, each making angle 45° and 135° with the positive X-axis is ______  


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 ______.


The combined equation of the lines which pass through the origin and each of which makes an angle of 30° with the line 3x + 2y – 11 = 0 is ______.


The line 5x + y – 1 = 0 coincides with one of the lines given by 5x2 + xy – kx – 2y + 2 = 0 then the value of k is ______.


Combined equation of the lines bisecting the angles between the coordinate axes, is ______.


Find the joint equation of the pair of lines through the origin and perpendicular to the lines given by 2x2 + 7xy + 3y2 = 0


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