Let one end of a focal chord of the parabola y^2=16x be (16,16). If P ( , ) divides this focal chord internally in the ratio 5 :2, then the minimum value of + is equal to:

Question

Accepted Answer

Correct answer: C. (c) Parabola y^2=16x ,a=4, focus at (4,0). Point (16,16) has parameter t_1=2. Other end of focal chord: t_2=-1/t_1=-1/2, giving (4 1/4 ,8 (-1/2 ) )= (1 ,-4 ). P divides the chord in ratio 5:2 internally (two cases): From (16 ,16 ) to (1 ,-4 ) :P= ( 377 , 127 ) , + =7. From (1 ,-4 ) to (16 ,16 ) :P= ( 827 , 727 ) , + =22. Minimum value of + =7.

$Let one end of a focal chord of the parabola y^{2} = 16 x be (16,16). If P (α, β) divides this focal chord internally in the ratio 5 : 2, then the minimum value of α + β is equal to:$

Solution

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