The equation of a directrix of the ellipse is
y = 25/3
x = 3
x = -3
x = 3/25
The length of the latus rectum of the hyperbola is
2a2/b
2b2/a
b2/a
a2/b
Sum of the focal distance of an ellipse is equal to
2 b
2 a
2 ab
a + b
The line y = 4x + c touches the hyperbola x2 - y2 = 1 iff
c = 0
c = ± √2
c = ± √15
c = ± √17
The diameter of 16x2 - 9y2 = 144 which is conjugate to x = 2y is
y = 16/9 x
y = 32/9 x
x = 16/9 y
x = 32/9 y
The latus rectum of the ellipse 5x2 + 9y2 = 45 is
10/3
5/3
5√5/3
10√5/3
Two diameters with slopes m1,m2 are conjugate if
m1m2 = -1
m1m2 = - b2/a2
m1m2 = a2/b2
m1m2 = b2/a2
The eccentricity of the conic 3x2 + 4y2 = 24 is
1/4
7/4
1/2
The line y = 2x + c touches the ellipse if c is equal to
0
± 2 √17
The locus of the points of intersection of perpendicular tangents to is
x2 + y2 = a2 + b2
x2 - y2 = a2 - b2
x2 + y2 = a2 - b2
x2 - y2 = a2 + b2