Question

The shortest distance between the line y = x and the curve y² = x - 2 is:
(A) 11/(4√2)
(B) 2
(C) 7/(4√2)
(D) 7/8

Answer 1

Answer:

refer to the attachment for solution

Answer 2

Correct option  (c)  7/4√2

Step-by-step explanation:

STEP : 1

Given equation in the question

y = x line  

$y^{2}$ = x – 2 parabola

for point P

STEP : 2

$(\frac{dy}{dx} )_{p} = 1$

$(\frac{1}{2y} )_{p} = 1$

$( y_{costiate} ) = \frac{1}{2}$

$( y_{coordinate} ) = \frac{9}{4}$

Point P $( \frac{9}{4} , \frac{1}{2} )$

STEP : 3

Shortest distance = perpendicular length  from P on line

x - y = 0

$= \frac{(\frac{9}{4} - \frac{1}{2} ) }{\sqrt{2} } }$

After solving above equation then we get

$= \frac{7}{4\sqrt{2} }$

Therefore the correct option is (c)  $= \frac{7}{4\sqrt{2} }$

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