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If P be a point on the parabola `y^2=3(2x-3)` and M is the foot of perpendiculardrawn from the point P on the directrix of the parabola, then length of each sides of an equilateral triangle SMP(where S is the focus of the parabola), isA. 2B. 4C. 6D. 8 |
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Answer» Correct Answer - C (3) `y^(2)=6(x-(3)/(2))` The equation of directrix is `x-(3)/(2)=-(3)/(2)orx=0` Vertex is `((3)/(2),0)` and focus of P be `((3)/(2)+(3)/(2)t^(2),3t)`. Then the coordinates of M are (0,3t). Therefore, `MS=sqrt(9+9t^(2))` `MP=(3)/(2)+(3)/(2)t^(2)` `or9+9t^(2)=((3)/(2)+(3)/(2)t^(2))^(2)=(9)/(4)(1+t^(2))^(2)` `or4=1+t^(2)` `:.` Length of side = 6 |
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