CAT 2017 Quantitative Ability

Start by finding the distance from some point on the curve to (2, 0) in terms of x Using the distance formula, we get

D=√(x−2)2+(√16x2+5x+16−0)2

D=√x2−4x+4+16x2+5x+16

D=√17x2+x+20

This will end up being a messy derivative. However, since the distance D will never be negative, we can minimize D2
instead of D and still get the same answer So, now we get

D2=17x2+x+20

‌‌

dD2

dx

=34x+1

Now we set this equal to 0 and solve for x
34x +1 = 0
x=−

1

34

So, the distance is minimized at x=−

1

34

and to find the minimum distance, simply evaluate D when x=−

1

34

∴‌‌D=√‌‌

17

(34)2

−‌‌

1

34

+20
=‌‌

1

34

√17−34+20×(34)2
=‌‌

1

34

√23103
≈ 4.4 units