Question

A point on the ellipse `x^2+3y^2=37` where the normal is parallel to the line `6x-5y=2` is `(5,-2)` (b) (5, 2) (c) `(-5,2)` (d) `(-5,-2)`
A. (5,-2)
B. (5,2)
C. (-5,2)
D. (-5,-2)

Answer 1

Differnetiating the equation of ellipse, `x^(2)+3y^(2)=37` w.r.t., x we get
`(dy)/(dx)=-(x)/(3y)`
The slop of the given line is 6/5 , which is normal to the ellipse
Hence, `3x//y=6//5 or 2x=5y`
Points in options (2) and (4) are satisfying the above equation adn that of ellipse.