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Two dimensional analytical geometry - class-XI
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Find $a$ if the distance between $(a , 2)$ and $(3 , 4)$ is $8 $
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A
$ 3 \, \pm \, \sqrt {60}$
💡 Explanation:
By square of distance formual:
$8^2=(3-a)^2+(4-2)^2$
$=>64=a^2-6a+13$
$=>a^2-6a-51=0$
solving the quadratic we get:
$a=(3+\sqrt(60)$ or $(3-\sqrt(60))$.