Ellipse questions
211 published questions with worked solutions.
- Let the length of a latus rectum of an ellipse x^2 a^2 + y^2 b^2 = 1 be 10. If its eccentricity is the minimum value of the...
- The locus of the foot of perpendicular drawn from the centre of the ellipse x^2 + 3y^2 = 6 on any tangent to it is:
- The eccentricity of an ellipse whose centre is at the origin is 1 2 . If one of its directrices is x = – 4, then the equation of...
- If the length of the latus rectum of an ellipse is 4 units and the distance between a focus and its nearest vertex on the major...
- If the tangents on the ellipse 4x^2 + y^2 = 8 at the points (1, 2) and (a, b) are perpendicular to each other, then a^2 is equal...
- In an ellipse, with centre at the origin, if the difference of the lengths of major axis and minor axis is 10 and one of the foci...
- If the line x − 2y = 12 is tangent to the ellipse x^2 a^2 + y^2 b^2 = 1 at the point (3, - 92 ), then the length of the latus...
- If the normal to the ellipse 3x^2 + 4y^2 = 12 at a point P on it is parallel to the line, 2x + y = 4 and the tangent to the...
- Let S and S′ be the foci of an ellipse and B be any one of the extremities of its minor axis. If ΔS′BS is a right angled triangle...
- Let the length of the latus rectum of an ellipse with its major axis along x-axis and centre at the origin, be 8. If the distance...
- If tangents are drawn to the ellipse x^2 + 2y^2 = 2 at all points on the ellipse other than its four vertices then the mid points...
- Let S = (x, y) R ^2 : y^2 1 + r - x^2 1 - r = 1 ; r ≠ ±1. Then S represents:
- An ellipse, with foci at (0, 2) and (0, −2) and minor axis of length 4, passes through which of the following points?
- If 3x+4y=12 2 is a tangent to the ellipse x^2 a^2 + y^2 9 =1 for some a R, then the distance between the foci of the ellipse is:
- The length of the minor axis (along y-axis) of an ellipse in the standard form is 4 3 . If this ellipse touches the line, x + 6y...
- If e_1 and e_2 are the eccentricities of the ellipse, x^2 18 + y^2 4 =1 and the hyperbola, x^2 9 - y^2 4 =1 respectively and...
- Let e_1 and e_2 be the eccentricities of the ellipse, x^2 25 + y^2 b^2 =1 (b < 5) and the hyperbola, x^2 16 - y^2 b^2 =1...
- Let P be a point on the ellipse x^2 9 + y^2 4 = 1. Let the line passing through P and parallel to y-axis meet the circle x² + y²...
- Let x^2 a^2 + y^2 b^2 = 1, a > b be an ellipse, whose eccentricity is 1 2 and the length of the latusrectum is 14 . Then the...
- If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12, then the length of its latus...
Other chapters
Alcohols, Phenols and EthersAldehydes, Ketones and Carboxylic AcidsAlternating CurrentAminesAnatomy of Flowering PlantsAncient Indian HistoryAnimal KingdomApplication of DerivativesArea Under CurveAromatic Compounds and Aryl HalidesAtomsBasic Mathematics and LogarithmBinomial TheoremBiodiversity and ConservationBiological ClassificationBiomoleculesBiotechnology and Its ApplicationsBiotechnology: Principles and ProcessesBody Fluids and CirculationBreathing and Exchange of GasesCell Cycle and Cell DivisionCell: The Unit of LifeChemical Bonding and Molecular StructureChemical Coordination and Integration