`(185)^2-(115)^2=`……………

A light ray coming along the line 3x+4y=5 gets reflected from the line a x+b y=1 and goes along the line 5x-12 y=10. Then, a=(64)/(115), b=(112)/(15) a=(14)/(15), b=-8/(115) a=(64)/(115), b=-8/(115) a=(64)/(15), b=(14)/(15)

If z_(1),z_(2)inC,z_(1)^(2)+z_(2)^(2)inR,z_(1)(z_(1)^(2)-3z_(2)^(2))=2 and z_(2)(3z_(1)^(2)-z_(2)^(2))=11, the value of z_(1)^(2)+z_(2)^(2) is

If a + ib = ((x+i)^2)/(2x^2+1) , prove that a^2+b^2 =((x^2+1)^2)/((2x^2+1)^2) .

Tangents at right angle are drawn to the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 . Show that the focus of the middle points of the chord of contact is the curve (x^(2)/a^(2)+y^(2)/b^(2))^(2)=(x^(2)+y^(2))/(a^(2)+b^(2)) .

The molar conductance of NaCl solution at different concentration at 298K are given below : {:(C(mol L^(-1)),wedge_(m)(S cm^(2)mol^(-1))),(0.001,123.7),(0.010,118.5),(0.020,115.75),(0.050,111.06):} Plot a graph between wedge_(m) and C^(1//2) and determine the value of wedge^(@)m from it.

Using the given pattern, find the missing numbers. 1^(2) + 2^(2) + 2^(2) = 3^(2) 2^(2) + 3^(2) + 6^(2) = 7^(2) 3^(2) + 4^(2) + 12^(2) = 13^(2) 4^(2) + 5^(2) + …^(2) = 21^(2) 5^(2) + ….^(2) + 30^(2) = 31^(2) 6^(2) + 7^(2) + .......^(2) = .........^(2)

In any triangle ABC, prove that : ((b^2-c^2))/a^2 sin 2A+ ((c^2-a^2))/b^2 sin 2B+ ((a^2-b^2))/c^2 sin2C=0 .