​​ Find the length of the chord of the ellipse x^2/25 + y^2/16 =1 whose middle point is (1/2,2/5)?

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Please find below the solution to the asked query:

x225+y216=1middle point is 12,25Let " T " be the equation of the chord .  Let " S " denote the equation of the ellipse .  Then the chord having its middle point as x1,y1 is given by T = S1 Here , T  xx125+yy116 - 1S1= x1225+y1216-1 Put , x1=12,y1=25 .  The equation of the chord is :x50+y40=x100+y1004x+5y200=21004x+5y=45y=4-4xy=451-xputting in eqn of ellipse:x225+y216=1x225+451-x216=1x225+1-x225=1x2+1+x2-2x25=12x2-2x+1=252x2-2x-24=0x2-x-12=0x2-4x+3x-12=0xx-4+3x-4=0x-4x+3=0hence, x=4 or x=-3for x=4y=451-x=451-4=-125for x=-3y=451-x=451+3=165hence end points are A4,-125B3,165AB=3+42+165+1252=49+78425=152009 unitssince we know equation of the chord

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