The equation of the ellipse whose centre is at the origin and the X -axis is major axis, which passes through the points (-3,1) and (2,-2) is

Step-by-step solution

Let equation of ellipse be x² a² + y² b² =1 Since it passes through the points (-3,1) and (2-2) aligned & (-3)² a² + (1)² b² =1 and (2)² a² + (-2)² b² =1 & 9 a² + 1 b² =1 ...(i) & 4 a² + 4 b² =1 ...(ii) aligned Multiply by 4 in Eq. (i) and subtracting Eq. (i) from Eq. (ii), 3 a²=32 a²= 32 3 Substituting in Eq. (i), gives aligned & 9 3 32 + 1 b² =1 & 1 b² =1- 27 32 = 5 32 b²= 32 5 aligned Required equation is 3 x² 32 + 5 y² 32 =1 or 3 x²+5 y²=32