The equation of the ellipse whose centre is at origin, major axis is along x -axis with eccentricity 3 4 and latus rectum 4 units is

Step-by-step solution

Given, b ^2=2 a , c ^2= ( 3 4 )^2 a ^2= 9 16 a ^2 We know, a^2=b^2+c^2 So, aligned a^2= & 2 a+ 9 16 a^2 16 a^2=32 a+9 a^2 7 a^2=32 a a= 32 7 & b^2= 64 7 aligned Equation of ellipse is x^2 a^2 + y^2 b^2 =1 x^2 ( 32 7 )^2 + y^2 64 7 =1 49 x^2 1024 + 7 y^2 64 =1