JEE Main 2019 — Hyperbola Questions with Solutions

The equation of a common tangent to the curves, y 2 = 16 x and x y = - 4 , is:

If the eccentricity of the standard hyperbola passing through the point ( 4,6 ) is 2 , then the equation of the tangent…

Let 0 < θ < π 2 . If the eccentricity of the hyperbola x 2 cos 2 ⁡ θ - y 2 sin 2 ⁡ &…

If a directrix of a hyperbola centered at the origin and passing through the point 4 , - 2 3 is 5 x = 4 5 and its eccen…

A hyperbola has its centre at the origin, passes through the point 4 ,   2 and has transverse axis of length 4 alo…

If the vertices of a hyperbola be at - 2 ,   0 and 2 ,   0 and one of its foci be at - 3 ,   0 , then wh…

If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13 , then the eccentric…

If 5 x + 9 = 0 is the directrix of the hyperbola 16 x 2 - 9 y 2 = 144 , then its corresponding focus is:

If the line y = m x + 7 3 is normal to the hyperbola x 2 24 - y 2 18 = 1 , then a value of m is:

The equation of a tangent to the hyperbola, 4 x 2 - 5 y 2 = 20 , parallel to the line x - y = 2 , is