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The vertices of a triangle ABC are A (0, 0), B (2, −1) and C (9, 2). Find cos B.
Concept: undefined >> undefined
Four points A (6, 3), B (−3, 5), C (4, −2) and D (x, 3x) are given in such a way that \[\frac{\Delta DBC}{\Delta ABC} = \frac{1}{2}\]. Find x.
Concept: undefined >> undefined
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The points A (2, 0), B (9, 1), C (11, 6) and D (4, 4) are the vertices of a quadrilateral ABCD. Determine whether ABCD is a rhombus or not.
Concept: undefined >> undefined
Find the coordinates of the centre of the circle inscribed in a triangle whose vertices are (−36, 7), (20, 7) and (0, −8).
Concept: undefined >> undefined
The base of an equilateral triangle with side 2a lies along the y-axis, such that the mid-point of the base is at the origin. Find the vertices of the triangle.
Concept: undefined >> undefined
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
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
