You should definitely improve the quality of the image, because I can't see anything clearly.
Also, the 4th answer is hidden.
Let the curve C be the intersection of the cylinder
and the plane
The projection of C on to the x-y plane is the ellipse
To see clearly that this is an ellipse, le us divide through by 16, to get
or
,
We can write the following parametric equations,
for
Since C lies on the plane,
it must satisfy its equation.
Let us make z the subject first,
This implies that,
We can now write the vector equation of C, to obtain,
The length of the curve of the intersection of the cylinder and the plane is now given by,
But
Therefore the length of the curve of the intersection intersection of the cylinder and the plane is 24.0878 units correct to four decimal places.
Here we have two right triangles. And in such case we have to use altitude rule which is
ratio of part of hypotenue and altitude= ratio of altitude and remaining part of hypotenuse
So we get
r/h =h/s
So the correct option is s .