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Find the distance between P (x1, y1) and Q (x2, y2) when (i) PQ is parallel to the y-axis (ii) PQ is parallel to the x-axis.
Concept: undefined >> undefined
Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).
Concept: undefined >> undefined
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Find the locus of a point equidistant from the point (2, 4) and the y-axis.
Concept: undefined >> undefined
Find the equation of the locus of a point which moves such that the ratio of its distances from (2, 0) and (1, 3) is 5 : 4.
Concept: undefined >> undefined
A point moves so that the difference of its distances from (ae, 0) and (−ae, 0) is 2a. Prove that the equation to its locus is \[\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\]
Concept: undefined >> undefined
Find the locus of a point such that the sum of its distances from (0, 2) and (0, −2) is 6.
Concept: undefined >> undefined
Find the locus of a point which is equidistant from (1, 3) and the x-axis.
Concept: undefined >> undefined
Find the locus of a point which moves such that its distance from the origin is three times its distance from the x-axis.
Concept: undefined >> undefined
A (5, 3), B (3, −2) are two fixed points; find the equation to the locus of a point P which moves so that the area of the triangle PAB is 9 units.
Concept: undefined >> undefined
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
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
