Correct option (a) and (b)
Explanation:
Let (x1 ,y1 ) be a point on ellipse then, x12 + 3y1 2 = 37 ...(1)
Equation of normal at (x1 ,y1 ) is a2x/x1 - b2y/y1 = a2 - b2
In ellipse x2/37 + y2/37/3 = 1
a2 = 37, b2 = 37/3
37x/x1 - 37y/3y1 = 37 - 37/3
37x/x1 - 37y/3y1 = 74/3 ...(2)
Slope of normal is
it is parallel to 6x – 5y + 7 = 0
3y1/x1 = 6/5
y1 = 2/5 x1
put in (1) we get
x21 + 12/25 x21 = 37
37x21/25 = 37
x21 = 25
x1 = ± 5
y1 =± 2
(5,2) & (–5,–2)