Tangents are drawn to the ellipse a2x2+b2y2=1 at two points whose eccentric angles are α−β and α+β The coordinates of their point of intersection are
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Two straight lines pass through the fixed points (±a,0) and have slopes whose products is p>0 Show that the locus of the points of intersection of the lines is a hyperbola.
If the tangents to the parabola y2=4ax
intersect the hyperbola a2x2−b2y2=1
, then find the locus of the point of intersection of the tangents at AandB˙
Find the eccentricity of the hyperbola given by equations x=2et+e−1andy=3et−e−1,t∈R˙
The lines parallel to the normal to the curve xy=1
Find the equation of the common tangent to the curves y2=8x and xy=-1.
(x-1)(y-2)=5 and (x−1)2+(y+2)2=r2 intersect at four points A, B, C, D and if centroid of △ABC lies on line y=3x−4 , then locus of D is
Find the equation of hyperbola :
Whose center is (1,0), focus is (6,0) and the transverse axis is 6
Find the vertices of the hyperbola 9x2−16y2−36x+96y−252=0