To find the area of the triangle formed by the pair of lines
23x2−48xy+3y2=0 with the line
2x+3y+5=0, consider the following:
Given parameters:
a=232h=−48 or h=−24b=3Coefficients of the line:
l=2,m=3,n=5The area of the triangle formed by the lines is calculated using the formula involving these parameters:
Calculate
n2√n2−ab :
n2=52=25ab=23×3=69n2−ab=25−69=−44Since this seems to be an error for the root, double-check the calculations based on the typical format. Typically, it should be deterministic for calculations.
Correct formula use for area
√am2−2hlm+l2b :
√am2−2hlm+l2b=√23×9+48×2×3+22×3=√23×9+48×2×3+4×3 =√23×9+288+12Full calculation and resolution:
Area =Correct simplification leads detailed steps as typically:
==After confirming detailed specific computations:
=Thus, the area of the triangle can be finally represented in the form that concludes the presentation: