MHT CET202613 April 2026Morning ShiftMathematicsStraight LinesActual
The area of the triangle formed by the co-ordinate axes and a line px + qy = r (where p, q and r are positive real numbers) is 1 54 sq.units, then ....
Options
- Ap, 3r, q are in G.P.
- Bp^2 + q^2 = r^2
- Cp, 3 3 r, q are in G.P.
- Dp, 27 r, q are in G.P.
Correct answer
C. p, 3 3 r, q are in G.P.
Step-by-step solution
The equation of the line is px + qy = r . The intercepts on the coordinate axes are r p and r q . The area of the triangle formed by the line and the coordinate axes is given by 1 2 base height . Area = 1 2 r p r q = r^2 2pq Given that the area is 1 54 sq. units, we have: r^2 2pq = 1 54 2pq = 54r^2 pq = 27r^2 pq = (3 3 r)^2 This satisfies the condition for p , 3 3 r , and q to be in Geometric Progression (G.P.). Answer: p, 3 3 r, q are in G.P.