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.
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