(4,9,12)

|{:(9,9,12),(1,-3,-4),(1,9,12):}|=0

Evaluate the following determinates |{:(-1,3,4),(1,9,12),(9,9,12):}|

Evalute |{:(3,6,9),(4,8,12),(5,10,5):}|

Evalute |{:(3,6,9),(4,8,12),(5,10,5):}|

{:(2,3,4),(4,6,8),(6,9,12),(36,81,underline(?)):}

Prove without expanding the determinant |(9, 9, 12),(1, -3, -4),(1, 9, 12)|=0 .

The ratio in which the point P(6,-6) divides the join of A(1,4) and B(9,-12) is

Numbers in follow questions have been arranged according to identical pattern. Find out the missing number {:(24,25,50),(24,20,10),(4,9,3),(12,5,?):}

S (3, 4) and S^(') (9, 12) are the focii of an ellipse and the foot of the perpendicular from S to a tangent to the ellipse is (1, -4). Then the eccentricity of the ellipse is