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Find the locus of a point such that the line segments with end points (2, 0) and (−2, 0) subtend a right angle at that point.
Concept: undefined >> undefined
If A (−1, 1) and B (2, 3) are two fixed points, find the locus of a point P, so that the area of ∆PAB = 8 sq. units.
Concept: undefined >> undefined
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A rod of length l slides between two perpendicular lines. Find the locus of the point on the rod which divides it in the ratio 1 : 2.
Concept: undefined >> undefined
Find the locus of the mid-point of the portion of the line x cos α + y sin α = p which is intercepted between the axes.
Concept: undefined >> undefined
If O is the origin and Q is a variable point on y2 = x, find the locus of the mid-point of OQ.
Concept: undefined >> undefined
What does the equation (x − a)2 + (y − b)2 = r2 become when the axes are transferred to parallel axes through the point (a − c, b)?
Concept: undefined >> undefined
What does the equation (a − b) (x2 + y2) −2abx = 0 become if the origin is shifted to the point \[\left( \frac{ab}{a - b}, 0 \right)\] without rotation?
Concept: undefined >> undefined
Find what the following equation become when the origin is shifted to the point (1, 1).
x2 + xy − 3x − y + 2 = 0
Concept: undefined >> undefined
Find what the following equation become when the origin is shifted to the point (1, 1).
x2 − y2 − 2x +2y = 0
Concept: undefined >> undefined
Find what the following equation become when the origin is shifted to the point (1, 1).
xy − x − y + 1 = 0
Concept: undefined >> undefined
Find what the following equation become when the origin is shifted to the point (1, 1).
xy − y2 − x + y = 0
Concept: undefined >> undefined
To what point should the origin be shifted so that the equation x2 + xy − 3x − y + 2 = 0 does not contain any first degree term and constant term?
Concept: undefined >> undefined
Verify that the area of the triangle with vertices (2, 3), (5, 7) and (− 3 − 1) remains invariant under the translation of axes when the origin is shifted to the point (−1, 3).
Concept: undefined >> undefined
Find what the following equation become when the origin is shifted to the point (1, 1).
x2 + xy − 3y2 − y + 2 = 0
Concept: undefined >> undefined
Find what the following equation become when the origin is shifted to the point (1, 1).
xy − y2 − x + y = 0
Concept: undefined >> undefined
Find what the following equation become when the origin is shifted to the point (1, 1).
xy − x − y + 1 = 0
Concept: undefined >> undefined
Find what the following equation become when the origin is shifted to the point (1, 1).
x2 − y2 − 2x + 2y = 0
Concept: undefined >> undefined
Find the point to which the origin should be shifted after a translation of axes so that the following equation will have no first degree terms: y2 + x2 − 4x − 8y + 3 = 0
Concept: undefined >> undefined
Find the point to which the origin should be shifted after a translation of axes so that the following equation will have no first degree terms: x2 + y2 − 5x + 2y − 5 = 0
Concept: undefined >> undefined
Find the point to which the origin should be shifted after a translation of axes so that the following equation will have no first degree terms: x2 − 12x + 4 = 0
Concept: undefined >> undefined
