Find the equation of the ellipse which passes through the points (-3,1) and (2,-2) , whose center lies at (0,0) and major axis lies along the X -axis.

Step-by-step solution

Centre and major axis of an ellipse are (0,0) and X -axis respectively. Let x^2 a^2 + y^2 b^2 =1 be the equation of ellipse. According to question it will pass through (-3,1) and (2,-2) 9 a^2 + 1 b^2 =1...(i) and 4 a^2 + 4 b^2 =1 1 a^2 + 1 b^2 = 1 4 ...(ii) Subtract Eq. (ii) from Eq. (i), we get 9 a^2 - 1 a^2 =1- 1 4 8 a^2 = 3 4 a^2= 32 3 By Eq. (i), we get array rlrl & & 9 32 3 + 1 b^2 & =1 & & 27 32 + 1 b^2 & =1 1 b^2 =1- 27 32 & 1 b^2 & = 32-27 32 & 1 b^2 = 5 32 b^2 & = 32 5 array array ll Equation of ellipse x^