AP EAMCET Coordinate Geometry: Hyperbola — practice questions
76 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice AP EAMCET Coordinate Geometry: Hyperbola in the app →The curve x²/16 − y²/9 = 1 has vertices on the x-axis. How far apart are they?Along the y-direction, x²/16 − y²/9 = 1 has a conjugate axis of what length?A hyperbola has a² = 16 and b² = 9 with its axis on the x-axis. Its e isWhere are the foci of x²/16 − y²/9 = 1?Compute 2b²/a for x²/16 − y²/9 = 1.Vertices are 3 units and foci 5 units from the centre on the x-axis. Which equation fits?Which lines does x²/9 − y²/4 = 1 approach far from its centre?For 9x² − 16y² = 144, the difference of focal distances of any point isFor a = 3 and b = 4 with a horizontal transverse axis, e equalsA horizontal hyperbola has c = 6 and e = 2. Which equation fits it?If e₁ and e₂ are eccentricities of a hyperbola and its conjugate, thenThe angle between asymptotes of a rectangular hyperbola isFind the foci of the hyperbola xy = 8.A general point on xy = c² isA parametric point of x²/a² − y²/b² = 1 isTangents of slope 1 to x²/16 − y²/9 = 1 areHow many real tangents can be drawn from an outside point to a hyperbola, in general?The combined equation of the asymptotes of x²/9 − y²/4 = 1 isA focus of x²/9 − y²/16 = 1 is at what distance from an asymptote?For x²/9 − y²/16 = 1, the product of distances from a point to both asymptotes isA focal chord perpendicular to the transverse axis of x²/9 − y²/16 = 1 measuresThe asymptotes make 60° with the transverse axis. The eccentricity isThe foci of y²/9 − x²/16 = 1 are atThe transverse axis of y²/25 − x²/9 = 1 lies along theThe centre of (x − 2)²/9 − (y + 1)²/4 = 1 isReduce 3x² − y² = 3 to standard form. What is its e?A rectangular hyperbola x² − y² = a² passes through (5, 3). Its transverse axis isA conic has eccentricity 1.5. It is aTwo hyperbolas have the same shape exactly when they share the sameA point moves so its distances from two fixed points differ by a constant less than their separation. Its locuA plane cuts both nappes of a double cone, missing the vertex. The section is aWho discovered hyperbolae while studying the doubling of the cube?How many vertices does a hyperbola have?The hyperbola x²/9 − y²/4 = 1 is symmetric aboutFor a point on a hyperbola, focal distance divided by directrix distance equalsA hyperbola and its conjugate always have the sameA focal chord at right angles to the axis of x² − y² = 25 measuresxy = 8 is a rectangular hyperbola. How far apart are its two vertices?The centre of the hyperbola (x − 1)(y − 2) = 3 isIf c = 8 and a = 6 for a horizontal hyperbola, what is b²?A hyperbola's latus rectum is half its transverse axis. Its eccentricity isWhich equation has e = 2 and foci 4 units either side of the centre, on the x-axis?How many points do x = 2 and x²/16 − y²/9 = 1 share?For which c does y = 2x + c touch x²/9 − y²/16 = 1?The normal to x²/a² − y²/b² = 1 at (x₁, y₁) isA comet exceeding the Sun's escape velocity follows aAt a point of a hyperbola, the tangent line bisects the angle betweenAt θ = 60° on x = 2 sec θ, y = 3 tan θ, the point isWith a = 7 and b = 24 on the transverse axis side, what is e?The vertices of y²/16 − x²/9 = 1 areFor y²/16 − x²/9 = 1, the lines approached far away areCompute 2b²/a for the vertical hyperbola y²/16 − x²/9 = 1.Asymptotes y = ±(3/4)x and vertex (4, 0) give the hyperbolaPut 2x² − 3y² = 6 in standard form and state its e.Reduce 2x² − 3y² = 6 and compute 2b²/a, its latus rectum.A hyperbola has transverse axis 12 and conjugate axis 10. Its eccentricity isA degenerate hyperbola reduces toThe linear eccentricity of x²/64 − y²/36 = 1 isA rectangular hyperbola has eccentricity equal toA hyperbola has a = 3 and eccentricity 2. What is the distance between its foci?The tangent to x²/a² − y²/b² = 1 at the point (x1, y1) has equationThe line y = mx + c touches the hyperbola x²/a² − y²/b² = 1 only ifThe tangents of slope 2 to the hyperbola x²/9 − y²/16 = 1 areA general point on the hyperbola x²/a² − y²/b² = 1 in parametric form isThe locus of a point whose distances from two fixed points differ by a constant is aThe eccentricity e of any hyperbola satisfiesThe midpoints of a family of parallel chords of a hyperbola lie on aA particle with total energy greater than zero moves under an inverse square attraction. Its path is aWhich Greek mathematician is believed to have coined the term hyperbola in his work on conic sections?What did early geometers call hyperbolas?The conjugate axis of a hyperbola has what length and direction?A hyperbola's eccentricity always satisfies which condition?A chord through a focus of a hyperbola, perpendicular to its major axis, is called what?LORAN fixes a ship on a hyperbola because it measures what?Confocal hyperbolas together with confocal ellipses form the basis of which two-dimensional coordinate system?The Greek word that gave ellipse its name has which meaning?