Q. 85.0( 1 Vote )
Write the area of the triangle formed by the coordinate axes and the line (sec θ – tan θ)x + (sec θ + tan θ) y = 2.
Answer :
Given:
Line (sec θ – tan θ)x + (sec θ + tan θ) y = 2.
To find:
The area of the triangle formed by the coordinate axes and the line (sec θ – tan θ)x + (sec θ + tan θ) y = 2.
Explanation:
The point of intersection of the coordinate axes is (0, 0).
Let us find the intersection of the line (sec θ − tan θ) x + (sec θ + tan θ) y = 2 and the coordinate axis.
For x-axis:
y = 0, x
For y-axis:
x = 0, y
Thus, the coordinates of the triangle formed by the coordinate axis and the line (sec θ − tan θ) x + (sec θ + tan θ) y = 2 are (0, 0), 
and 
.
Let A be the area of the required triangle.
∴ A
⇒ A
⇒ A
Hence, the area of the triangle is 2 square units.
Rate this question :
Various Forms of Equations of line45 mins
Parametric Equations of Straight line48 mins
Slope, inclination and angle between two lines48 mins
Interactive Quiz on Equations of line23 mins
Straight line | Analyse your learning through quiz56 mins
General Equation of a line43 mins
Motion in a Straight Line - 0665 mins
Motion in a Straight Line - 0556 mins
Motion in a Straight Line - 0372 mins
Understand The Interesting Concept Of Relative velocity in 1- Dimension44 mins
Find the equation of the line drawn through the point of intersection of the lines x + y = 9 and 2x – 3y + 7 = 0 and whose slope is 
.
Find the equation of the line drawn through the point of intersection of the lines x – y = 7 and 2x + y = 2 and passing through the origin.
RS Aggarwal - MathematicsFind the equation of the line drawn through the point of intersection of the lines x – 2y + 3 = 0 and 2x – 3y + 4 = 0 and passing through the point (4, -5).
RS Aggarwal - MathematicsFind the equation of the line through the intersection of the lines 2x – 3y + 1 = 0 and x + y – 2 = 0 and drawn parallel to y-axis.
RS Aggarwal - MathematicsFind the equation of the line through the intersection of the lines x – 7y + 5 = 0 and 3x + y – 7 = 0 and which is parallel to x-axis.
RS Aggarwal - MathematicsFind the equation of the line through the intersection of the lines 2x – 3y = 0 and 4x – 5y = 2 and which is perpendicular to the line x + 2y + 1 = 0.
RS Aggarwal - MathematicsFind the equation of the line through the intersection of the lines 5x – 3y = 1 and 2x + 3y = 23 and which is perpendicular to the line 5x – 3y = 1.
RS Aggarwal - MathematicsFind the equation of the line drawn through the point of intersection of the lines x – y = 1 and 2x – 3y + 1 = 0 and which is parallel to the line 3x + 4y = 12.
RS Aggarwal - MathematicsFind the equation of the line passing through the intersection of the lines 2x + y = 5 and x + 3y + 8 = 0 and parallel to the line 3x + 4y = 7.
RD Sharma - MathematicsProve that the lines 
, 
, 
and 
form a rhombus.
