TS EAPCET (Engineering) Circle — practice questions
84 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice TS EAPCET (Engineering) Circle in the app →A circle has its centre at the origin and radius r. Which equation represents it?The equation x² + y² + 2gx + 2fy + c = 0 represents a real circle when which condition holds?A second degree equation is a circle only if what holds?Diameter ends are (1, 2) and (5, 6). What is the circle?Circle on diameter ends (x₁, y₁), (x₂, y₂) has which equation?What is the equation of the circle with centre (3, 4) that passes through the origin?What are the parametric equations of the circle x² + y² = r²?Which is a parametric form of the circle (x − 3)² + (y + 2)² = 16?A line that meets a circle in two coincident points is called what?Find the tangent to x² + y² = 25 at the point (3, 4).What is the tangent at (x₁, y₁) to x² + y² + 2gx + 2fy + c = 0?How many tangents can be drawn to a circle from a point outside it?The line y = mx + c touches x² + y² = a² when which condition holds?For which values of c is y = x + c a tangent to x² + y² = 8?The line 3x − 4y + 15 = 0 touches x² + y² = r². What is r?Which circle x² + y² = r² is touched by the line 4x + 3y = 10?Slopes of the two tangents from an external point P(x₁, y₁) to a circle satisfy what kind of equation in m?For the circle x² + y² = 4, find the product of slopes of tangents from (3, 1).The locus of the point of intersection of perpendicular tangents to a circle is called what?What is the director circle of x² + y² = a²?A circle has radius 5. What is the radius of its director circle?If tangents from P are perpendicular, what is the product of their slopes m₁m₂?What is the equation of the circle through (5, 7), (6, 6) and (2, −2)?The points (3, −2), (1, 0), (−1, −2), (1, −4) lie on a circle with which centre?Points that all lie on one circle are described as what?A circle with centre (−3, 3) touches the Y-axis at (0, 3). What is its equation?Find the circle with centre (4, −1) that touches the Y-axis.What name is given to the form (x − h)² + (y − k)² = r²?Expanding the circle with centre (h, k) and radius r, what is the constant c in the general form?Two diameters of a circle are 2x + y = 6 and 3x + 2y = 4. What is its centre?For x² + y² − 2x + 4y + k = 0 to be a real circle, which must hold?What does x² + y² + 2x − 4y + 5 = 0 represent?A circle centred at the origin passes through (6, 8). What is its radius?The point on x² + y² = 9 given by parameter θ = 90° is which?Which point on x² + y² = 16 corresponds to θ = 60°?A tangent to a circle is always perpendicular to which line at the point of contact?What is the equation of the director circle of x² + y² − 2x − 4y − 4 = 0?Which axis does the circle x² + y² + 4x − 6y + 4 = 0 touch?The circle x^2 + y^2 - 6x + 8y = 0 has radiusA circle has a diameter with ends (0, 0) and (6, 8). Its centre isAmong all chords of a circle, the longest one isTwo chords of a circle are equidistant from its centre exactly when they areAn angle inscribed in a semicircle measuresA chord subtends 80 degrees at the centre. The inscribed angle on the major arc isTwo angles stand on the same chord but lie on opposite sides of it. Their sum isIn a cyclic quadrilateral, an exterior angle is equal to theA tangent at point P on a circle with centre O is, relative to radius OP,Two tangents are drawn to a circle from an outside point. Their lengths areTwo chords cross inside a circle. One is cut into 6 and 4, the other into 3 and x. Find x.From an outside point a secant cuts a circle with distances 4 and 9 from the point. The tangent length isIn a circle of radius 7, a chord subtends 90 degrees at the centre. Its length isThe sagitta of a circle is also known as theA chord is 8 long and its sagitta is 2. The radius of the circle isPoints equally distant from two fixed points A and B formWhich of these polygons can always be circumscribed by a circle?Among plane shapes of equal perimeter, the greatest area is enclosed by theArchimedes matched a circle's area to a triangle with base equal to the circumference and height equal to theAn arc of length 12 cm on a circle of radius 6 cm subtends a central angle ofThe Egyptian Rhind papyrus method for a circle's area corresponds to pi being aboutWhich book of Euclid's Elements deals with the properties of circles?The region bounded by two concentric circles is called anA line meeting a circle in two points, an extended chord, is called aThe region common to two overlapping discs is called aA region bounded by a chord and one of its arcs is called aIn strict usage, a circle is only which part of a disc?A circle whose radius is zero reduces toA circle has radius 7 cm. Its circumference isIf a circle's radius is doubled, its enclosed area becomesA tangent to a circle has how many points in common with it?The equation of the unit circle centred at the origin isWith x = r cos t and y = r sin t, r = 5, which point lies at t = 90 degrees?In the complex plane, |z - 2| = 3 describes a circle with centreIn polar coordinates, a circle with its centre at the pole and radius 4 has equationThe tangent to x^2 + y^2 = 25 at (3, 4) has slopeHow many circles pass through the collinear points (1, 2), (2, 4) and (3, 6)?Two perpendicular chords are cut into 2 and 6, and 3 and 4. The diameter squared isTwo secants meet outside a circle and cut off arcs of 100 and 40 degrees. The angle isTangents from P touch a circle at A and B, and angle APB is 70 degrees. Angle AOB at the centre isThe smallest circle through both ends of a 10 cm chord AB has radiusThe centre of the circle through three non-collinear points is where these lines meetTo construct a circle on a given diameter, its centre is taken at the diameter'sA plane cuts a double cone at right angles to its axis. The section is aA circle is the locus of points in a plane that areThe circle (x - 3)^2 + (y - 4)^2 = 25 passes through which point?