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Let line L₁ be the reflection of a tangent to the parabola (y-2)^2=4(x-1) drawn at P in the line x=1 . If area of the triangle formed by the line L₁ , the tangent and straight line y=2 is 64 sq . units, then find the abscissa of point P .

Correct answer

17

Step-by-step solution

aligned y^2 & =4 x & =P (a t^2, 2 a t ) aligned Tangent at P . aligned t Y & =X+t^2 Q & (-t^2, 0 ), R (t^2, 0 ) aligned Area of P Q R, 1 2 2 t^2 t= 64 t= 4 Now, abscissa of point P x-1=16 x=17

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