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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
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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
Verify that the area of the triangle with vertices (4, 6), (7, 10) and (1, −2) remains invariant under the translation of axes when the origin is shifted to the point (−2, 1).
Concept: undefined >> undefined
The vertices of a triangle are O (0, 0), A (a, 0) and B (0, b). Write the coordinates of its circumcentre.
Concept: undefined >> undefined
In Q.No. 1, write the distance between the circumcentre and orthocentre of ∆OAB.
Concept: undefined >> undefined
Write the coordinates of the orthocentre of the triangle formed by points (8, 0), (4, 6) and (0, 0).
Concept: undefined >> undefined
Three vertices of a parallelogram, taken in order, are (−1, −6), (2, −5) and (7, 2). Write the coordinates of its fourth vertex.
Concept: undefined >> undefined
If the points (a, 0), (at12, 2at1) and (at22, 2at2) are collinear, write the value of t1 t2.
Concept: undefined >> undefined
If the coordinates of the sides AB and AC of ∆ABC are (3, 5) and (−3, −3), respectively, then write the length of side BC.
Concept: undefined >> undefined
Write the coordinates of the circumcentre of a triangle whose centroid and orthocentre are at (3, 3) and (−3, 5), respectively.
Concept: undefined >> undefined
Write the coordinates of the in-centre of the triangle with vertices at (0, 0), (5, 0) and (0, 12).
Concept: undefined >> undefined
If the points (1, −1), (2, −1) and (4, −3) are the mid-points of the sides of a triangle, then write the coordinates of its centroid.
Concept: undefined >> undefined
Write the area of the triangle with vertices at (a, b + c), (b, c + a) and (c, a + b).
Concept: undefined >> undefined
Taking the set of natural numbers as the universal set, write down the complements of the following set:
{x : x is an odd natural number}
Concept: undefined >> undefined
Taking the set of natural numbers as the universal set, write down the complements of the following set:
{x : x is a positive multiple of 3}
Concept: undefined >> undefined
Taking the set of natural numbers as the universal set, write down the complements of the following set:
{x : x is a prime number}
Concept: undefined >> undefined
Taking the set of natural numbers as the universal set, write down the complements of the following set:
{x : x is a natural number divisible by 3 and 5}
Concept: undefined >> undefined
Taking the set of natural numbers as the universal set, write down the complements of the following set:
{x : x is a perfect square}
Concept: undefined >> undefined
