The ellipse 25x2+16y2=1 and the hyperbola 25x2−16y2=1 have in common
Tangents are drawn from the points on a tangent of the hyperbola x2−y2=a2 to the parabola y2=4ax˙ If all the chords of contact pass through a fixed point Q, prove that the locus of the point Q for different tangents on the hyperbola is an ellipse.
Let P be a point on the hyperbola x2−y2=a2, where a is a parameter, such that P is nearest to the line y=2x˙ Find the locus of P˙
If values of a, for which the line y=ax+25 touches the hyperbola 16x2−9y2=144 are the roots of the equation x2−(a1+b1)x−4=0, then the values of a1+b1 is
For hyperbola whose center is at (1, 2) and the asymptotes are parallel to lines 2x+3y=0 and x+2y=1 , the equation of the hyperbola passing through (2, 4) is (2x+3y−5)(x+2y−8)=40 (2x+3y−8)(x+2y−8)=40 (2x+3y−8)(x+2y−5)=30 none of these
The equation of the transvers and conjugate axes of a hyperbola are, respectively, x+2y−3=0 and 2x−y+4=0 , and their respective lengths are 2 and 23˙ The equation of the hyperbola is 52(x+2y−3)2−53(2x−y+4)2=1 52(x−y−4)2−53(x+2y−3)2=1 2(2x−y+4)2−3(x+2y−3)2=1 2(x+2y−3)2−3(2x−y+4)2=1