Let P ( 4 , 4 3 ) be a point on the parabola y 2 = 4 a x and PQ be a focal chord of the parabola. If M and N are the foot of perpendiculars drawn from P and Q respectively on the directrix of the pa

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Let P ( 4 , 4 3 ​ ) be a point on the parabola y 2 = 4 a x and PQ be a focal chord of the parabola. If M and N are the foot of perpendiculars drawn from P and Q respectively on the directrix of the parabola, then the area of the quadrilateral PQMN is equal to :

TestHub · Accepted Answer

​ ( 4 , 4 3 ​ ) lies on y 2 = 4 ax ⇒ 48 = 4 a ⋅ 4 4 a = 12 ​ ⇒ y 2 = 12 x is equation of parabola Now, parameter of P is t 1 ​ = 3 ​ 2 ​ ⇒ Parameters of Q is t 2 ​ = − 2 3 ​ ​ ⇒ Q ( 4 9 ​ , − 3 3 ​ ) Area of trapezium PQNM ​ = 2 1 ​ MN ⋅ ( PM + QN ) = 2 1 ​ MN ⋅ ( PS + QS ) = 2 1 ​ MN ⋅ PQ = 2 1 ​ 7 3 ​ ⋅ 4 49 ​ = ( 343 ) 8 3 ​ ​ ​

Mathematics - Parabola Question with Solution | TestHub

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