AP EAMCET Coordinate Geometry: Ellipse — practice questions
80 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice AP EAMCET 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 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 isThe sum of distances from two fixed points is constant. The locus is:Kepler's first law says each planet moves in an ellipse with the Sun at:Who named the ellipse, from the Greek for omission, in his Conics?If the two foci of an ellipse coincide, the curve becomes a:In the directrix definition, distance to focus divided by distance to directrix is the:The tangent at a point of an ellipse is the external bisector of the lines to the:A ray leaving one focus of an ellipse reflects off it and passes through the:The orthoptic circle of an ellipse is another name for its:A gardener fixes two pegs and a rope to outline an elliptical bed. Each peg is a:An ellipse x²/a² + y²/b² = 1 passes through (3, 2). It must also pass through:A plane misses the apex of a cone and is less steep than its lines. The section is:In x = a cos t, y = b sin t, the parameter t is called the:For x = 4 cos t, y = 3 sin t, the point at t = π/3 is:In an elliptical room, a whisper at one focus is heard clearly at the:The area enclosed by x²/49 + y²/25 = 1 is:Unlike its area, the exact perimeter of an ellipse needs:The foci of 25x² + 169y² = 4225 are:An ellipse with foci (±4, 0) and focal distances adding to 10 has equation:An ellipse has minor axis 12 and e = 4/5. Its major axis is:The directrices of x²/25 + y²/9 = 1 are the lines:Centred at origin, an ellipse cuts the axes at (±6, 0) and (0, ±3). Equation:P lies on x²/81 + y²/45 = 1. Its focal distances add to:Line y = x + k touches x²/9 + y²/4 = 1. Possible k:An ellipse with a = 4 and e = 1/2 has a latus rectum of length:With semi-major axis 10 and e = 0.6, the distance between foci is:A point of an ellipse with e = 1/2 is 8 units from a directrix. Focal distance:x²/(k-2) + y²/(5-k) = 1 is an ellipse for:The ellipse x²/a² + y²/b² = 1 becomes a circle when:Two pins and a taut string trace an ellipse. What do the pins mark?A ray from one focus of an elliptical mirror reflects. Where does it go?For a point on an ellipse, the ratio of its distance from a focus to its distance from the directrix is calledA circle is an ellipse whose two foci are placed how?What is the chord through one focus, perpendicular to the major axis, of an ellipse called?Waves start at one focus of an elliptical water tank and bounce off the walls. Where do they meet?