TS EAPCET (Engineering) Locus (mathematics) — practice questions
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Practice TS EAPCET (Engineering) Locus (mathematics) in the app →The locus of points equidistant from two intersecting lines isA circle is the locus of points at a constant distance fromPoints whose distances from two foci add up to a constant form aIn the parabola as a locus, the fixed line is called theThe word locus comes from Latin, where it meansThe set of points where a function takes the value zero is itsThe set of critical points of a differentiable function is called itsThe singular locus is the set of singular points of anThe Mandelbrot set is characterised as a locus of which type?Proving that a shape is the correct locus is usually split into how many stages?One stage of a locus proof shows every point satisfying the conditionsA point moves so that PA/PB is a constant k other than 1. Its locus is aA point is always equally far from A(2, 0) and B(-2, 0). Its locus isA point stays 5 units from the origin. Its locus isP is as far from (0, 2) as from the line y = -2. Its locus isDistances of P from (3, 0) and (-3, 0) add to 10. Locus of P isWith A(0, 0) and B(3, 0), P moves so that PA = 2PB. The locus is a circle of radiusThe midpoint of the segment from the origin to a point of x^2 + y^2 = 16 lies onA point has coordinates (t, 2t + 1) as t varies. Its locus isWith A and B fixed, medians from A and C of triangle ABC are perpendicular. Locus of C is aFor PA = 3PB with A(-1, 0), B(0, 2), the locus circle has centrePoints exactly 3 units from the x-axis lie onLines from P to (-2, 0) and (2, 0) are perpendicular. P lies onWith AB fixed, C moves so triangle ABC has constant area. C lies onIn a translation of axes, the new x' axis is what relative to the x axis?What stays fixed when the coordinate axes are rotated?A rotation of axes is classified as which type of transformation?The origin is shifted to (h, k). Old and new coordinates are related byThe origin is shifted to (-1, 4). The point (2, 6) now has coordinatesShifting the origin to (2, -3) turns x^2 + y^2 - 4x + 6y - 3 = 0 intoTo remove the first-degree terms of x^2 + y^2 + 2x - 4y + 1 = 0, shift the origin toTranslating to (-1, 2) reduces 9x^2+25y^2+18x-100y-116=0 to an ellipse with a =The ellipse 9x^2+25y^2+18x-100y-116=0 has eccentricityThe vertex of the parabola y^2 - 4y - 8x + 12 = 0 isThe centre of the circle x^2 + y^2 - 6x + 4y - 12 = 0 isWhich algebraic technique mainly simplifies second-degree equations by translation?Axes are rotated through theta. The old x in terms of new coordinates isAxes turn 90 degrees anticlockwise. The point (3, 4) gets new coordinatesWhich term can a suitable rotation of axes remove from a second-degree equation?Rotating axes through 45 degrees changes xy = 1 intoThe axes are rotated through any angle. The circle x^2 + y^2 = 9 becomesWhich expression keeps its value when axes are rotated about the origin?When axes are translated, the slope of a given lineIn three dimensions the origin moves to (h, k, l). Old z equalsA second-degree equation in x, y, z that is not a cylinder, plane, line or point gives aIf axes are rotated counterclockwise, a fixed point appears rotatedIf axes shift h to the right and k up, a fixed point appears movedThe foci of the ellipse 9x^2+25y^2+18x-100y-116=0 are