The longest distance of the point (a, 0) from the curve 2 x^2+y^2=2 x is

Step-by-step solution

Given, curve is 2 x^2+y^2=2 x2 x^2-2 x+y^2=0 2 (x- 1 2 )^2+y^2= 1 2 (x- 1 2 )^2 1 4 + y^2 1 2 =1 which represents an ellipse. Here, a= 1 2 , b= 1 2 , h= 1 2 , k=0 Consider a point P(h+a , k+b )=P ( 1 2 + 1 2 , 1 2 ) on the ellipse from which the distance of point (a, 0) is maximum. let Q(a, 0) Now, P Q= ( 1 2 + 1 2 -a )^2+ ( 1 2 -0 )^2 = 1 4 + 1 4 ^2 +a^2+ 1 2 -a -a+ 1 2 ^2 P Q= 1 2 +a^2-a+ ( 1 2 -a ) + 1 4 ^2 Let y=P Q^2= 1 2 +a^2-a+ ( 1 2 -a ) + 1 4 ^2 For maxima and minima, put d y d =0 - ( 1 2 -a ) + 1 4 2 =0 (