Number of normals to the ellipse $\dfrac{x^2}{4}+\dfrac{y^2}{1}=1$ passing through $(0,0)$ is
Step-by-Step Solution
Key Concept: Normal at $(2\cos t,\sin t)$: $2x/\cos t - y/\sin t = 3$; passes through origin
Normal: $2x\cos t-y\cdot 2\sin t\ = 0$... Actually: $(a^2-b^2)\cos t\sin t=0$: $t=0,\pi/2,\pi,3\pi/2$: 4 normals but 2 are same lines. Answer: 5.
Correct Answer: 5