CAT Exam Model Paper 1 with solutions for free online practice

Question : 82 of 100

Marks: +1, -0

Find the shortest distance from the point (5,0) to the curve

2y^{2} = x ^{3}

Solution:

d = √ { ( x - 5 ) ^ { 2 } + ( y - 0 ) ^ { 2 } }

d =√ { ( x - 5 ) ^ { 2 } + y ^ { 2 } }

from

2 y ^ { 2 } = x ^ { 3 } , y ^ { 2 } = { 1 } /{ 2 } x ^ { 3 }

d = √ { ( x - 5 ) ^ { 2 } + { 1 } /{ 2 } x ^ { 3 } }

{ d d }/ { d x } = { 2 ( x - 5 ) + { 3 }/ { 2 } x ^ { 2 } }/ { 2 √ { ( x - 5 ) ^ { 2 } + { 1 } /{ 2 } x ^ { 3 } } } = 0

{ 3 }/ { 2 } x ^ { 2 } + 2 x - 10 = 0

3 x ^ { 2 } + 4 x - 20 = 0

( 3 x + 10 ) ( x - 2 ) = 0

For 3x + 10 = 0, x =

-10/3

For x − 2 = 0, x = 2[For minimum]
Use x = 2

d = √ { ( 2 - 5 ) ^ { 2 } + { 1 }/ { 2 } ( 2 ^ { 3 } ) }

d = \√ { 13 }

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