if the normal at any point P meets the major and minor axes at G and G1 and OF be the perpendicular upon this normal then show that PF.PG=b^2 and PF.PG1=a^2.

Question

Chetan Mandayam Nayakar · Answer

let P be (x0,y0),x 2 /a 2 + y 2 /b 2 =1,implicit diferentiation yields 2x/a 2 +2yy'/b 2 =0, y'=-(xb 2 )/(ya 2 )...equation(1),equation of normal= (y-y0)/(x-x0)=-1/y', major axis is y=0,solve equation of normal and y=0 to get G. similarly find G1 perpendicular upon normal is given by (y/x)=y'...equation(2),solve (1) and (2) to find F

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if the normal at any point P meets the major and minor axes at G and G1 and OF be the perpendicular upon this normal then show that PF.PG=b^2 and PF.PG1=a^2.

if the normal at any point P meets the major and minor axes at G and G1 and OF be the perpendicular upon this normal then show that PF.PG=b^2 and PF.PG1=a^2.

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if the normal at any point P meets the major and minor axes at G and G1 and OF be the perpendicular upon this normal then show that PF.PG=b^2 and PF.PG1=a^2.

if the normal at any point P meets the major and minor axes at G and G1 and OF be the perpendicular upon this normal then show that PF.PG=b^2 and PF.PG1=a^2.

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