Application of Derivatives Part 1

Shortest distance between two curve occurred along the common normal
Slope of normal to y2=x at point
P(t2,t) is −2t and
slope of line y−x=1 is 1 .
As they are perpendicular to each other
‌∴(−2t)=−1⇒t=‌

1

2

‌∴P(‌

1

4

,‌

1

2

)
and shortest distance =|‌

‌ 1 2 − 1 4 −1

√2

‌

‌

| So shortest distance between them is ‌

3√2

8