Question
Question: The area of the quadrilateral formed by the tangents at the end points of the latus rectum to the el...
The area of the quadrilateral formed by the tangents at the end points of the latus rectum to the ellipse 9x2+5y2=1, is
Solution
We know that the ends of latus rectum of an ellipse a2x2+b2y2=1 are (±ae,ab2). We know that tangent of ellipse a2x2+b2y2=1 at (x1,y1) is a2xx1+b2yy1=1. We know that there will be four latus rectums for an ellipse. So, the area of a quadrilateral ellipse formed by all the latus rectums is equal to 4 times of the area of the triangle formed by a single latus rectum. So, we can find the area of the quadrilateral formed by the tangents at the end points of the latus rectum to the ellipse 9x2+5y2=1
Complete step-by-step answer:
We know that the eccentricity of ellipse a2x2+b2y2=1 is equal to 1−a2b2.
Now we should find the eccentricity of 9x2+5y2=1.
Let us compare a2x2+b2y2=1 with 9x2+5y2=1.
Then we get