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Question: The distance between the points \((am_{1}^{2},2am_{1})\) and \((am_{2}^{2},2am_{2})\) is....

The distance between the points (am12,2am1)(am_{1}^{2},2am_{1}) and

(am22,2am2)(am_{2}^{2},2am_{2}) is.

A

a(m1−m2)(m1+m2)2+4a(m_{1} - m_{2})\sqrt{(m_{1} + m_{2})^{2} + 4}

B

(m1−m2)(m1+m2)2+4(m_{1} - m_{2})\sqrt{(m_{1} + m_{2})^{2} + 4}

C

a(m1−m2)(m1+m2)2−4a(m_{1} - m_{2})\sqrt{(m_{1} + m_{2})^{2} - 4}

D

(m1−m2)(m1+m2)2−4(m_{1} - m_{2})\sqrt{(m_{1} + m_{2})^{2} - 4}

Answer

a(m1−m2)(m1+m2)2+4a(m_{1} - m_{2})\sqrt{(m_{1} + m_{2})^{2} + 4}

Explanation

Solution

s=(am12−am22)2+(2am1−2am2)2s = \sqrt { \left( a m _ { 1 } ^ { 2 } - a m _ { 2 } ^ { 2 } \right) ^ { 2 } + \left( 2 a m _ { 1 } - 2 a m _ { 2 } \right) ^ { 2 } }

=a(m1−m2)(m1+m2)2+4= a \left( m _ { 1 } - m _ { 2 } \right) \sqrt { \left( m _ { 1 } + m _ { 2 } \right) ^ { 2 } + 4 }.