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Circles and tangents Question If from any point on the circle x 2  + y 2  +2gx + 2fy + c = 0, tangents are drawn to the circle x 2  + y 2  + 2gx + 2fy + csin 2 α + (g 2 + f 2 )cos 2 α = 0, then angle between the tangents is  Concepts used - Circle with equation x 2  + y 2  + 2gx + 2fy + c = 0, has center at (-g,-f) and radius √(g 2 +f 2 -c), √  (g 2 +f 2 -c)  - sin 2  + cos 2 = 1 Answer Rearrange the equation of circles to find the centers and radii Circle 1 - x 2  + y 2  +2gx + 2fy + c = 0 x 2  + y 2  +2gx + 2fy + c = 0 x 2  + y 2  +2gx + 2fy + g 2  + f 2 = g 2  + f 2 - c  (x+g) 2  + (x+f) 2 = (√(g 2 +f 2 -c)) 2 Circle 2 - x 2  + y 2  + 2gx + 2fy + csin 2 α + (g 2  + f 2 )cos 2 α = 0 x 2  + y 2  + 2gx + 2fy + g 2  + f 2 = g 2  + f 2 - csin 2 α - (g 2 ...

If x,y and z are 3 numbers such that x+y+z=5, x>3, y>0, z>0 and the maximum value of (x-3)(2y+1)(3z+5) is 6(m/n) 3 , here m and n are co-prime numbers, then the value of 18(m/n) is Can anyone help me in solving this?

A particle is moving in a straight line with initial velocity u and retardation av, where v is the velocity at any time t [a] the particle will cover a total distance u/a  [b] the particle will come to rest after 1/a  [c] the particle will continue to move for a very long time  [d] the velocity of the particle will become u/2 after time 1/a Solution: