मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

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

Advertisements
Advertisements

प्रश्न

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

पर्याय

  • `4/sqrt3` sq units

  • `8/sqrt3` sq units

  • `16/sqrt3` sq units

  • `15/sqrt3` sq units

MCQ
Advertisements

उत्तर

The area of triangle formed by the lines x2 + 4xy + y2 = 0 and x - y - 4 = 0 is `8/sqrt3` sq units.

shaalaa.com
  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 1.1 | 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 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 - 4xy = 0 


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

x2 + 2(cosec α)xy + 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:

The combined equation of the coordinate axes is


Choose correct alternatives:

If h2 = ab, then slopes of lines ax2 + 2hxy + by2 = 0 are in the ratio


Choose correct alternatives:

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


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 origin and having inclinations 60° and 120°.


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 which are at a distance of 9 units from the Y-axis.


Show that the following equations represents a pair of line:

x2 + 2xy - y2 = 0


Show that the following equations represent a pair of line:

x2 - y2 = 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:

6x2 - 5xy - 6y2 = 0


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

x2 - 4y2 = 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 three times the other.


If the line 4x - 5y = 0 coincides with one of the lines given by ax2 + 2hxy + by2 = 0, then show that 25a + 40h + 16b = 0


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

2x2 + xy - y2 + x + 4y - 3 = 0


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


Find the condition that the equation ay2 + bxy + ex + dy = 0 may represent a pair of lines. 


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.


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.


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


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


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


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 ______.


If `x^2/a + y^2/b + (2xy)/h` = 0 represents a pair of lines and slope of one line is twice the other, then find the value of ab : h2.


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


Find the combined equation of y-axis and the line through the origin having slope 3.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×