Question

Using lagrange's multiplier method find the shortest distance between the line y 10 2x and the ellipse 2 2 1

Answer 1

Answer:

Can you please check your question once.

Answer 2

Answer:

Alternatively: you can find the tangent line to the ellipse that is parallel to the line y=10−2x.

The tangent line to the ellipse at the point (x0,y0) must have the slope −2:

(x24+y29)′x=(1)′x⇒x2+2y9y′=0⇒y′=−9x4y⇒

y′(x0)=−9x0±4⋅31−x204−−−−−√=−2⇒x0=±85⇒y0=±95.

Note: In general, there can be two tangent lines and x0=−85,y0=−95 must be ignored as it is the furthest point from the given line (i.e. the max distance).

Then you should find the distance from the point (85,95) of ellipse to the line y=10−2x.