Let P be point on the graph of a straight line y=2x−3 and Q be a point on the graph of a parabola y=x^2 +x+1 .Find the shortest distance between P and Q .


Question and Answers Forum

All Questions Topic List
Differentiation Questions
Previous in All Question Next in All Question
Previous in Differentiation Next in Differentiation
Question Number 126605 by bramlexs22 last updated on 22/Dec/20

$L e t P b e p o i n t o n t h e g r a p h$ $o f a s t r a i g h t l i n e y = 2 x - 3 a n d Q$ $b e a p o i n t o n t h e g r a p h o f a p a r a b o l a$ $y = x^{2} + x + 1 . F i n d t h e s h o r t e s t$ $d i s t a n c e b e t w e e n P a n d Q .$
	Answered by liberty last updated on 22/Dec/20

	$l e t y = 2 x + p i s t a n g e n t l i n e a t c u r v e$ $y = x^{2} + x + 1 \Rightarrow w e g e t 2 x + 1 = 2; x = \frac{1}{2}$ $t h e p o i n t Q (\frac{1}{2}, \frac{7}{4}) a n d p = \frac{3}{4}$ $t h u s ∣ P Q ∣_{m i n} = ∣ \frac{\frac{3}{4} - (- 3)}{\sqrt{5}} ∣ = \frac{15}{4 \sqrt{5}} = \frac{3}{4} \sqrt{5}$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum