Question

. What does the equation of the st. lines 7x2 + 4xy + 4y2 = 0 become when the axes are
the bisectors of the angles between them?
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Answer 1

Answer:

What does the equation of the straight lines 7x2+4xy+4y2=0 become when the axes are the bisectors of the angles between them?

My Attempt:

7x2+4xy+4y2=0

Comparing the above equation with ax2+2hxy+by2=0 we get a=7, h=2 and b=4.

If α be the angle between the lines represented by the given equation, we write:

tan α=2h2−ab−−−−−−√a+b

tan α=24−28−−−−−√7+4

tan α=2−24−−−−√11

hope it's helpful

Answer 2

Answer:

The concept of transformation of axes and equation of bisector of ax^2+2hxy+by^2=0 has been used here.

Two answers you will get which depends on the bisector equation you have taken. 1. 8x^2+3y^2=0    2. 15x^2-4xy+40y^2=0

Step-by-step explanation:

I have mentioned only one  solution, the other can be done in the same pattern.