MHT-CET Conic Sections — practice questions
67 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice MHT-CET Conic Sections in the app →Conic sections are curves formed when a plane cuts which solid?A plane cuts one nappe of a cone at 90 degrees to its axis. The section is aIf alpha < beta < 90 degrees and the plane cuts one nappe, the curve is aA plane parallel to a generator of the cone (beta = alpha) gives aA plane cutting both nappes of a cone produces which curve?The vertex of a double cone separates it into two parts calledThe rotating line that sweeps out a double cone is called itsA plane passes through the cone's vertex with alpha < beta <= 90 degrees. The section isA plane through the vertex contains a generator of the cone. The section isWhich degenerate section is the degenerate case of a hyperbola?Which equation gives a circle with centre (h, k) and radius r?The circle x² + y² + 8x + 10y - 8 = 0 has which centre and radius?If the fixed point lies on the fixed line, the equal-distance locus isThe axis of a parabola is the line through the focus that isThe point where a parabola meets its axis is called theFor the parabola y² = 4ax with a > 0, the focus is atThe directrix of the parabola y² = 4ax with a > 0 is the lineThe latus rectum of the parabola y² = 4ax has lengthThe parabola y² = 8x has its focus at which point?What is the latus rectum length for the parabola y² = 8x?Which parabola has focus (2, 0) and directrix x = -2?Which parabola has vertex (0, 0) and focus (0, 2)?A parabola y² = 4ax has a latus rectum of length 12. What is a?An ellipse is the set of points whose distances from two fixed points have a constantThe mid point of the segment joining the foci of an ellipse is itsThe segment of an ellipse passing through both foci is called theThe segment through the centre perpendicular to the major axis is theThe end points of the major axis of an ellipse are called itsIn standard notation, the minor axis of an ellipse has lengthIn standard notation, the distance between the two foci of an ellipse isFor an ellipse with semi-axes a and b and focal distance c, which relation holds?If an ellipse has eccentricity e and semi-major axis a, each focus is how far from the centre?Where are the foci of the ellipse x²/25 + y²/9 = 1?What is the minor axis length of the ellipse 9x² + 4y² = 36?The latus rectum of an ellipse with semi-axes a and b has lengthAn ellipse has vertices (±13, 0) and foci (±5, 0). Its equation isAn ellipse has semi-major axis 13 and semi-minor axis 12. How far apart are its foci?The constant sum of focal distances on an ellipse is always what compared to the distance between the foci?A non-degenerate conic with eccentricity exactly 1 is aEccentricity of an ellipse measures how far the ellipse deviates from beingHow many branches does a hyperbola have?A hyperbola is the locus of points where which quantity for two foci is constant?The parabola y² = 4ax with a > 0 extends indefinitely into which quadrants?Latus rectum length of y² = 20x is?Vertex of (x + 2)² = −4(y + 3) is?Focal distance of P(x₁, y₁) on y² = 4ax?Which conic has e = 1?Tangent to y² = 8x at (2, 4)?y = mx + c touches y² = 4ax if?Parametric point of y² = 4ax?Point t = 2 on y² = 4x?Tangents from an outside point to a parabola?Focus to directrix distance, y² = 6x?y² = 4ax is symmetric about?Eccentricity range of an ellipse?Major axis of x²/25 + y²/9 = 1?Focal distance sum on x²/16 + y²/9 = 1?Directrices of x²/25 + y²/9 = 1?Auxiliary circle of x²/a² + y²/b² = 1?Ellipse relation of b, a and e?Ellipse a = 5, e = 3/5. Minor axis?Foci and directrices of an ellipse?Hyperbola x²/a² − y²/b² = 1 gives?Conjugate axis of x²/9 − y²/16 = 1?Circle on transverse axis as diameter?Locus with ratio e > 1 to a directrix?Transverse axis of x²/49 − y²/25 = 1?