A line passing through the point A ( − 2 , 0 ) , touches the parabola P : y 2 = x − 2 at the point B in the first quadrant. The area, of the region bounded by the line AB , parabola P and the x -axis,

Question

A line passing through the point A ( − 2 , 0 ) , touches the parabola P : y 2 = x − 2 at the point B in the first quadrant. The area, of the region bounded by the line AB , parabola P and the x -axis, is :-

TestHub · Accepted Answer

Tangent ​ y = m ( x + 2 ) y 2 = x − 2 ( m ( n + 2 ) ) 2 = n − 2 m 2 x 2 + ( 4 m 2 − 1 ) x + ( 4 m 2 + 2 ) = 0 D = 0 ( 4 m 2 − 1 ) 2 − 4 m 2 ( 4 m 2 + 2 ) = 0 m = 4 1 ​ y = 4 1 ​ ( n + 2 ) ​ and point of tangency ( 6 , 2 ) ​ Area A = ∫ 0 2 ​ ( ( y 2 + 2 ) − ( 4 y − 2 ) ) d y A = 3 8 ​ ​ option (3)

Mathematics - Parabola Question with Solution | TestHub

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