The equation of an ellipse in its standard form, given the distance between its foci is 2 units and the length of its latusrectum is 15 2 units, is

Step-by-step solution

Standard form of ellipse, x^2 a^2 + y^2 b^2 =1 a > b Distance between foci =2 a e 2 = 2ae a e=1 ...(ii) aligned & and length of latusrectum = 2 b^2 a & aligned 15 2 & = 2 b^2 a b^2= 15 a 4 b^2 & =a^2 (-e^2+1 )=-a^2 e^2+a^2 15 a 4 & =-1+a^2 aligned aligned aligned & 4 a^2-15 a-4=0 & 4 a^2-16 a+a-4=0 & 4 a(a-4)+(a-4)=0 &(4 a+1)(a-4)=0 & a=-1 / 4 and 4 aligned When, a = + 4 b^2= 15 a 4 = 15 4 4 b= 15 Equation of ellipse, x^2 16 + y^2 15 =1 15 x^2+16 y^2=240