TS EAPCET (Engineering) Coordinate Geometry: Ellipse — practice questions
47 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice TS EAPCET (Engineering) Coordinate Geometry: Ellipse in the app →What is the length of the major axis of the ellipse x²/25 + y²/9 = 1?For an ellipse with semi-axes a > b and focal distance c, which relation holds?For any point on an ellipse with semi-major axis a, the sum of its distances from the foci equalsThe eccentricity e of an ellipse always satisfiesThe ellipse with foci (±3, 0) and semi-major axis 5 has equationThe distance between the foci of 9x² + 16y² = 144 isAn ellipse has a major axis of 10 and a minor axis of 8. Its eccentricity isFor a point on x²/36 + y²/20 = 1, the sum of its distances from the two foci isWhich point lies on the ellipse x²/9 + y²/4 = 1?If b² = a²/2 for an ellipse, its eccentricity isAn ellipse has foci (0, ±4) and minor axis of length 6. Its equation isThe foci of an ellipse are 8 apart and its major axis is 10. Its eccentricity isWhat is the eccentricity of the ellipse 9x² + 25y² = 225?Distance from (0, 3) to a focus of x²/25 + y²/9 = 1 isThe major axis lies along the y-axis for the ellipseThe ellipse 25x² + 16y² = 400 has a major axis of lengthFor a point on the ellipse 16x² + y² = 16, the sum of focal distances isTwo fixed points are 6 apart and a moving point keeps its distance sum at 10. The minor axis isIf the constant distance sum equals the gap between the two fixed points, the locus isHow many axes of symmetry does an ellipse x²/a² + y²/b² = 1 (a ≠ b) have?An ellipse has a = 10 and e = 0.6. Each focus is how far from the centre?Which ellipse is closest in shape to a circle?Which value can be the eccentricity of an ellipse?The foci of an ellipse are (-2, 3) and (6, 3). Its centre isFoci (-2, 3) and (6, 3), distance sum 10. What is the minor axis length?If the major axis is twice the minor axis, the eccentricity isThe latus rectum of an ellipse isAn oval garden has a 20 m major axis and a 12 m minor axis. How far apart are its foci?A taut 20 cm string is tied to two pins 12 cm apart and a pencil traces an ellipse. Its semi-minor axis isA centred ellipse has axes along the coordinate axes and passes through (5, 0) and (0, 3). Where are its foci?To read off a and b from 9x² + 16y² = 144, divide both sides byP lies on an ellipse of major axis 20 and PF1 = 7. What is PF2?A point is 3 units from one focus of x²/25 + y²/9 = 1. Its distance from the other focus isFor x²/16 + y²/b² = 1 to have e = √7/4, the value of b² isThe ellipse x²/a² + y²/4 = 1 has foci (±√5, 0). Find a.An ellipse has latus rectum 3 and eccentricity 1/2. Its semi-major axis isThe vertices are (0, ±10) and e = 4/5. Where are the foci?If the focus is 3 from the centre and the semi-minor axis is 4, the major axis isIs the point (2, 3) inside, on or outside x²/16 + y²/9 = 1?Where is (1, 1) relative to the ellipse x²/16 + y²/9 = 1?The minor axis equals the distance between the foci. The eccentricity isA is a point on x²/25 + y²/9 = 1 and F1, F2 are the foci. The perimeter of triangle AF1F2 isFor which k does x²/k + y²/9 = 1 have foci (±4, 0)?The semi-axes of 4x² + 9y² = 1 have lengthsThe ordinate of the point of x²/25 + y²/9 = 1 above focus (4, 0) isAn ellipse with e = 4/5 and semi-minor axis 3 has semi-major axisFor e = 3/5, the major axis to minor axis ratio is