If 2x−y+1=0 is a tangent to the hyperbola a2x2−16y2=1 then which of the following CANNOT be sides of a right angled triangle? (a)a,4,2 (b) a,4,1(c)2a,4,1 (d) 2a,8,1
An ellipse has eccentricity 21 and one focus at the point P(21,1). Its one directrix is the comionand tangent nearer to the point the P to the hyperbolaof x2−y2=1 and the circle x2+y2=1.Find the equation of the ellipse.
A variable chord of the hyperbola a2x2−b2y2=1,(b>a), subtends a right angle at the center of the hyperbola if this chord touches. a fixed circle concentric with the hyperbola a fixed ellipse concentric with the hyperbola a fixed hyperbola concentric with the hyperbola a fixed parabola having vertex at (0, 0).
From the point (2, 2) tangent are drawn to the hyperbola 16x2−9y2=1. Then the point of contact lies in the first quadrant (b) second quadrant third quadrant (d) fourth quadrant
The distance between two directrices of a rectangular hyperbola is 10 units. Find the distance between its foci.
Each of the four inequalities given below defines a region in the xy plane. One of these four regions does nothave the following property. For any two points (x1,y2)and(y1,y2) in the region the piont (2x1+x2⋅2y1+y2) is also in the region. The inequality defining this region is