Let S be the set of all a ∈ N such that the area of the triangle formed by the tangent at the point P b , c , b , c ∈ N , on the parabola y 2 = 2 a x and the lines x = b , y = 0 is 16 unit 2 , then ∑ a ∈ S a is equal

Question

Let S be the set of all a &#8712; N such that the area of the triangle formed by the tangent at the point P b , c , b , c &#8712; N , on the parabola y 2 = 2 a x and the lines x = b , y = 0 is 16 unit 2 , then &#8721; a &#8712; S a is equal to _____ .

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Given, S be the set of all a &#8712; N such that the area of the triangle formed by the tangent at the point P b , c , &#160; b , &#160; c &#8712; N , on the parabola y 2 = 2 a x And the lines x = b , y = 0 is 16 unit 2 Now plotting the diagram we get, Tangent at P b , c will be a x - c y + a b = 0 and it meets x -axis at - b , 0 Now area of triangle P A B = 1 2 2 b c = 16 &#8658; b c = 16 So, b , c = 1 , 16 , 2 , 8 , 4 , 4 , 8 , 2 , 16 , 1 as both belongs to natural number, Now b , c lie on parabola hence satisfy

Let S be the set of all a ∈ N such that the area of the triangle formed by the tangent at the point P b , c , b , c ∈ N , on the parabola y 2 = 2 a x and the lines x = b , y = 0 is 16 unit 2 , then ∑ a ∈ S a is equal to _____ .

Correct answer

Step-by-step solution

More from Parabola

Let S be the set of all a &#8712; N such that the area of the triangle formed by the tangent at the point P b , c , b , c &#8712; N , on the parabola y 2 = 2 a x and the lines x = b , y = 0 is 16 unit 2 , then &#8721; a &#8712; S a is equal to _____ .

Correct answer

Step-by-step solution

More from Parabola

Let S be the set of all a ∈ N such that the area of the triangle formed by the tangent at the point P b , c , b , c ∈ N , on the parabola y 2 = 2 a x and the lines x = b , y = 0 is 16 unit 2 , then ∑ a ∈ S a is equal to _____ .