Let the harmonic mean and geometric mean of two positive numbers be the ratio 4 : 5. Then the two number are in the ratio .........

If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is

Determine all values of $$\alpha $$ for which the point $$\left( {\alpha ,\,{\alpha ^2}} \right)$$ lies insides the triangle formed by the lines $$$\matrix{ {2x + 3y - 1 = 0} \cr {x + 2y - 3 = 0} \cr {5x - 6y - 1 = 0} \cr } $$$

The centre of a circle passing through the points (0, 0), (1, 0) and touching the circle $${x^2} + {y^2} = 9$$is