Circles Part 1

As per question area of one sector =3 area of another sector
⇒ at center by one sector =3× angle at center by another sector
Let one angle be θ then other =30
Clearly θ+3θ=180⇒θ=45∘
∴ Angle between the diameters represented by combined equation
ax2+2(a+bxy)+by2=0 is 45∘
∴ Using tan‌θ=‌

2√h2−ab

a+b

we get tan‌45∘=‌

2√(a+b)2−ab

a+b

⇒1=‌

2√a2+b2+ab

a+b

⇒(a+b)2=4(a2+b2+ab)
⇒a2+b2+2ab=4a2+4b2+4ab
⇒3a2+3b2+2ab=0