PUC Science Class 11 - Karnataka Board PUC Question Bank Solutions

For the ellipse 12x² + 4y² + 24x − 16y + 25 = 0

The equation of the ellipse with focus (−1, 1), directrix x − y + 3 = 0 and eccentricity 1/2 is

The equation of the circle drawn with the two foci of \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\] as the end-points of a diameter is

The eccentricity of the ellipse \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\] if its latus rectum is equal to one half of its minor axis, is

The eccentricity of the ellipse, if the distance between the foci is equal to the length of the latus-rectum, is

The eccentricity of the ellipse, if the minor axis is equal to the distance between the foci, is

The difference between the lengths of the major axis and the latus-rectum of an ellipse is

The eccentricity of the conic 9x² + 25y² = 225 is

The latus-rectum of the conic 3x² + 4y² − 6x + 8y − 5 = 0 is

The equations of the tangents to the ellipse 9x² + 16y² = 144 from the point (2, 3) are

The eccentricity of the ellipse 4x² + 9y² + 8x + 36y + 4 = 0 is

The eccentricity of the ellipse 4x² + 9y² = 36 is

The eccentricity of the ellipse 5x² + 9y² = 1 is

For the ellipse x² + 4y² = 9

If the latus rectum of an ellipse is one half of its minor axis, then its eccentricity is

An ellipse has its centre at (1, −1) and semi-major axis = 8 and it passes through the point (1, 3). The equation of the ellipse is

The sum of the focal distances of any point on the ellipse 9x² + 16y² = 144 is

If (2, 4) and (10, 10) are the ends of a latus-rectum of an ellipse with eccentricity 1/2, then the length of semi-major axis is

The equation \[\frac{x^2}{2 - \lambda} + \frac{y^2}{\lambda - 5} + 1 = 0\] represents an ellipse, if

The eccentricity of the ellipse 9x² + 25y² − 18x − 100y − 116 = 0, is