CBSE (Commerce) Class 12CBSE
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

Find the Coordinates of a Point on the Parabola Y=X2+7x + 2 Which is Closest to the Strainght Line Y = 3x − 3 ? - CBSE (Commerce) Class 12 - Mathematics

Login
Create free account


      Forgot password?

Question

Find the coordinates of a point on the parabola y=x2+7x + 2 which is closest to the strainght line y = 3x \[-\] 3 ?

Solution

\[\text { Let coordinates of the point on the parabola be } \left( x, y \right) . \text { Then }, \]

\[y = x^2 + 7x + 2 ............. \left( 1 \right)\]

\[\text { Let the distance of a point } \left( x, \left( x^2 + 7x + 2 \right) \right) \text { from the line } y = 3x - 3\text {  be S . Then,} \]

\[S = \left| \frac{- 3x + \left( x^2 + 7x + 2 \right) + 3}{\sqrt{10}} \right|\]

\[ \Rightarrow \frac{dS}{dt} = \frac{- 3 + 2x + 7}{\sqrt{10}}\]

\[\text { For maximum or minimum values of S, we must have }\]

\[\frac{dS}{dt} = 0\]

\[ \Rightarrow \frac{- 3 + 2x + 7}{\sqrt{10}} = 0\]

\[ \Rightarrow 2x = - 4\]

\[ \Rightarrow x = - 2\]

\[\text { Now }, \]

\[\frac{d^2 S}{d t^2} = \frac{2}{\sqrt{10}} > 0\]

\[\text { So, the nearest point is} \left( x, \left( x^2 + 7x + 2 \right) \right) . \]

\[ \Rightarrow \left( - 2, 4 - 14 + 2 \right)\]

\[ \Rightarrow \left( - 2, - 8 \right)\]

  Is there an error in this question or solution?

Video TutorialsVIEW ALL [1]

Solution Find the Coordinates of a Point on the Parabola Y=X2+7x + 2 Which is Closest to the Strainght Line Y = 3x − 3 ? Concept: Graph of Maxima and Minima.
S
View in app×