Given that x and y vary so that ax + by= c , where a,b,c are constant. Show that the minimum value of x^2 + y^2 is c^2/ a^2 + b^2 ?
2 Answers
The minimum value is
Explanation:
The minimum of
Then
substituting this value into
Also
Explanation:
Let
Point in the Plane
If
a Family of Lines in the plane, where,
Let us note that,
Now, the Distance
Accordingly, when
Thus, in this new scenario, our Problem is to find the
Minimum Distance from the Origin
From Geometry, we know that the minimum distance of a point
them, given by,
Accordingly,
We conclude with a note that, in case,
Enjoy Maths.!