The abscissae of two points A and B are the roots of the equation x2 + 2ax – b2 = 0 and their ordinates are the roots of y2 + 2py – q2 = 0 then the distance AB in terms of a, b, p, q is

Let x1 , x2 are x-coordinates of A, B and y1 , y2 are y-coordinates of A, B then AB2=x1−x22+y1−y22=x1+x22-4x1x2+(y1+y2)2-4y1y2 =4a2 +4b2 +4p2 +4q2

The abscissae of two points A and B are the roots of the equation x2 + 2ax – b2 = 0 and their ordinates are the roots of y2 + 2py – q2 = 0 then the distance AB in terms of a, b, p, q is

Let x1 , x2 are x-coordinates of A, B and y1 , y2 are y-coordinates of A, B then AB2=x1−x22+y1−y22=x1+x22-4x1x2+(y1+y2)2-4y1y2 =4a2 +4b2 +4p2 +4q2

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The abscissae of two points A and B are the roots of the equation x² + 2ax – b² = 0 and their ordinates are the roots of y² + 2py – q² = 0 then the distance AB in terms of a, b, p, q is

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$\sqrt{a^{2} + b^{2} + p^{2} + q^{2}}$

$2 \sqrt{a^{2} + b^{2} + q^{2} + p^{2}}$

$\sqrt{a^{2} + b^{2} + p^{2}}$

$\sqrt{a^{2} + b^{2} + q^{2}}$

answer is B.

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Detailed Solution

Let x₁ , x₂ are x-coordinates of A, B and y₁ , y₂ are y-coordinates of A, B then $A B^{2} = {(x_{1} - x_{2})}^{2} + {(y_{1} - y_{2})}^{2} = {(x_{1} + x_{2})}^{2} - 4 x_{1} x_{2} + {(y_{1} + y_{2})}^{2} - 4 y_{1} y_{2} = 4 a^{2} + 4 b^{2} + 4 p^{2} + 4 q^{2}$