Question

For the ellipse \[ \frac{x^2}{36}+\frac{y^2}{25}=1, \] the straight line \[ 2x+y-5=0 \] is

• A. a tangent
• B. a normal
• C. a focal chord
• D. a chord not passing through its foci

Hint:

For the ellipse \[ \frac{x^2}{a^2}+\frac{y^2}{b^2}=1, \] the line \[ y=mx+c \] is tangent if \[ \boxed{c^2=a^2m^2+b^2.} \] If this condition is not satisfied but the line intersects the ellipse at two points, it is a chord.

Answer 1

The Correct Option is D