alleryStart learning →The hyperbola (x + 3)²/16 - (y - 1)²/9 = 1 is centred at the new origin
- (3, 1)
- (-3, -1)
- (-3, 1)
- (3, -1)
Show answer and solution
Correct answer: C. (-3, 1)
The centre makes x + 3 = 0 and y - 1 = 0, giving (-3, 1).
AP EAMCET Coordinate Geometry: Transformation of Axes — practice questions — page 2
Explore 51 free Coordinate Geometry: Transformation of Axes questions in AP EAMCET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 31–51 of 51.
The hyperbola (x + 3)²/16 - (y - 1)²/9 = 1 is centred at the new originRead the answer and worked solution →The points (1, 2) and (4, 6) are 5 apart. After shifting the origin, their distance isRead the answer and worked solution →The origin is moved to (4, 0). The line 3x + 4y = 12 becomesRead the answer and worked solution →The origin is first moved to (1, 2), then a further (3, -1) from there. The net origin isRead the answer and worked solution →With new origin (h, k), a point (x, y) has new coordinatesRead the answer and worked solution →Axes are turned 45° counterclockwise. The line y = x becomesRead the answer and worked solution →The origin moves to (3, 5). Where is the old origin in the new system?Read the answer and worked solution →Moving the origin to (3, 4) changes x² + y² = 25 intoRead the answer and worked solution →Translating to the centre turns x² + 4y² - 2x + 8y + 1 = 0 intoRead the answer and worked solution →When axes are rotated about the z axis in 3D, each point's z coordinateRead the answer and worked solution →Why are coordinate axes often moved relative to a curve?Read the answer and worked solution →For studying an ellipse, the foci are usually placedRead the answer and worked solution →In a rotation of axes, which point is kept fixed?Read the answer and worked solution →Which kind of axis change gives new axes parallel to the original ones?Read the answer and worked solution →Which kind of axis change keeps the origin fixed and turns the axes?Read the answer and worked solution →A rotation of axes is chosen for a general second degree equation to remove which term?Read the answer and worked solution →After shifting the origin, which terms can vanish when there is no xy term?Read the answer and worked solution →The axes are shifted 2 units right and 3 units up. A point at (5, 7) in the old system has what new coordinates?Read the answer and worked solution →If the origin is moved to the point (h, k) with axes kept parallel, what is the old x in terms of the new x'?Read the answer and worked solution →With the origin moved to (1, -2), x^2 + y^2 = 25 becomes what?Read the answer and worked solution →For the curve xy = 8, the origin is moved to (2, 1). What is the transformed equation?Read the answer and worked solution →
Worked practice questions
The points (1, 2) and (4, 6) are 5 apart. After shifting the origin, their distance is
- 7
- 3
- 4
- 5
Show answer and solution
Correct answer: D. 5
Translation is a rigid transformation, so the distance sqrt(9 + 16) = 5 does not change.
The origin is moved to (4, 0). The line 3x + 4y = 12 becomes
- 3x' + 4y' = 24
- 3x' - 4y' = 0
- 3x' + 4y' = 12
- 3x' + 4y' = 0
Show answer and solution
Correct answer: D. 3x' + 4y' = 0
Substituting x = x' + 4 gives 3x' + 12 + 4y' = 12, so 3x' + 4y' = 0.
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