The combined equation of the two diameters of a circle which divide the circle into 4 sectors is ax^2+2hxy+by^2=0. If the area of the bigger sector is…

Question

The combined equation of the two diameters of a circle which divide the circle into 4 sectors is ax^2+2hxy+by^2=0. If the area of the bigger sector is 5 times the area of the smaller sector, then a+b√(a-b^2+4h^2)=

MARKS Content Team · Accepted Answer

Correct answer: (B) √32. Let angle between given pair of lines is θ according to given information. A_2=5A_1 1/2×π-θr^2=1/2×θr^2×5 π-θ=5θ θ=(π)/6 ∵cos(π)/6=a+b√(a-b^2+2h^2) √32=a+b√(a-b^2+4h^2) ∴a+b√(a-b^2+4h^2)=√32

The combined equation of the two diameters of a circle which divide the circle into $4$ sectors is $a x^{2} + 2 h x y + b y^{2} = 0$ . If the area of the bigger sector is $5$ times the area of the smaller sector, then $\frac{|a + b|}{\sqrt{{(a - b)}^{2} + 4 h^{2}}} =$

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Relevant Questions

The combined equation of the two diameters of a circle which divide the circle into 4 sectors is ax2+2hxy+by2=0. If the area of the bigger sector is 5 times the area of the smaller sector, then a+ba-b2+4h2=

Solution

Relevant Questions

The combined equation of the two diameters of a circle which divide the circle into $4$ sectors is $a x^{2} + 2 h x y + b y^{2} = 0$ . If the area of the bigger sector is $5$ times the area of the smaller sector, then $\frac{|a + b|}{\sqrt{{(a - b)}^{2} + 4 h^{2}}} =$