AP EAPCET (Engineering) Coordinate Geometry: Transformation of Axes — practice questions
43 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice AP EAPCET (Engineering) Coordinate Geometry: Transformation of Axes in the app →Axes are moved so the new origin is (-1, 4). Find the new coordinates of (3, 2).After shifting the origin to (1, 2), a point has new coordinates (4, 5). Its old coordinates areOrigin shifted to (2, -1). What does y = 2x + 3 become in the new axes?Shifting the origin to (1, 1) turns x² + y² - 2x - 2y - 2 = 0 intoMoving the origin to (2, 2) reduces y² - 4y - 8x + 20 = 0 to which form?To remove the first-degree terms of x² + y² + 6x - 8y = 0, move the origin toThe origin should be moved to which point to remove x and y terms of 3x² + 2y² - 6x + 8y - 1 = 0?When axes are translated, the coefficients of x², xy and y² in a second-degree equationWhich statement holds for a translation of axes in the plane?Which is true of a rotation of axes about the origin?Axes are shifted 3 units right and 2 units up. A fixed point P then appears movedIf the axes are rotated counterclockwise through an angle, a fixed point appears rotatedA rotation of axes in a second-degree equation is chosen to eliminate theAfter the xy term is gone, a translation of axes removes which terms?Which algebraic method is used with a translation to simplify a conic equation?In 3D, a new origin for a translation of axes is given by how many coordinates?A second-degree equation in x, y, z that is not a cylinder, plane, line or point gives aAxes are rotated 90° counterclockwise. The point (3, 4) gets new coordinatesAfter the axes turn through 180°, the point (3, -5) has coordinatesAfter a 90° counterclockwise axes rotation, a point is (2, 5) in the new system. Originally it wasRotating the axes by 45° changes 3x² + 2xy + 3y² = 8 intoThe curve xy = 8 is rotated by turning the axes through 45°. Its new equation isThe curve 2x² + xy + 3y² = 6 is of which type?The curve x² + 3xy + y² = 5 is aThe curve 4x² + 4xy + y² + 2x = 0 represents aFor axes rotated counterclockwise by θ, the old x equalsThe point (3, 4) is distance D from the origin. After any rotation of axes, D isIn a shift of origin to (h, k), the new x' axis is parallel to x and lies how far away?In a translation of axes, the positive x' and y' directions are taken to beThe ellipse (x - 2)²/9 + (y + 1)²/4 = 1 takes standard form with origin atThe hyperbola (x + 3)²/16 - (y - 1)²/9 = 1 is centred at the new originThe points (1, 2) and (4, 6) are 5 apart. After shifting the origin, their distance isThe origin is moved to (4, 0). The line 3x + 4y = 12 becomesThe origin is first moved to (1, 2), then a further (3, -1) from there. The net origin isWith new origin (h, k), a point (x, y) has new coordinatesAxes are turned 45° counterclockwise. The line y = x becomesThe origin moves to (3, 5). Where is the old origin in the new system?Moving the origin to (3, 4) changes x² + y² = 25 intoTranslating to the centre turns x² + 4y² - 2x + 8y + 1 = 0 intoWhen axes are rotated about the z axis in 3D, each point's z coordinateWhy are coordinate axes often moved relative to a curve?For studying an ellipse, the foci are usually placedIn a rotation of axes, which point is kept fixed?