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A line perpendicular to the line segment joining the points (1, 0) and (2, 3) divides it in the ratio 1:n. Find the equation of the line.
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Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3).
Concept: undefined >> undefined
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Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.
Concept: undefined >> undefined
Find equation of the line through the point (0, 2) making an angle `(2pi)/3` with the positive x-axis. Also, find the equation of line parallel to it and crossing the y-axis at a distance of 2 units below the origin.
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The perpendicular from the origin to a line meets it at the point (– 2, 9), find the equation of the line.
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The length L (in centimetre) of a copper rod is a linear function of its Celsius temperature C. In an experiment, if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L in terms of C
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The owner of a milk store finds that, he can sell 980 litres of milk each week at Rs 14/litre and 1220 litres of milk each week at Rs 16/litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at Rs 17/litre?
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P (a, b) is the mid-point of a line segment between axes. Show that equation of the line is `x/a + y/b = 2`
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Point R (h, k) divides a line segment between the axes in the ratio 1:2. Find equation of the line.
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By using the concept of equation of a line, prove that the three points (3, 0), (–2, –2) and (8, 2) are collinear.
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Find the values of q and p, if the equation x cos q + y sinq = p is the normal form of the line `sqrt3 x` + y + 2 = 0.
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Find the area of the triangle formed by the lines y – x = 0, x + y = 0 and x – k = 0.
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Find the image of the point (3, 8) with respect to the line x + 3y = 7 assuming the line to be a plane mirror.
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If the lines y = 3x + 1 and 2y = x + 3 are equally inclined to the line y = mx + 4, find the value of m.
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A point is on the x-axis. What are its y-coordinates and z-coordinates?
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A point is in the XZ-plane. What can you say about its y-coordinate?
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The coordinates of points in the XY-plane are of the form _______.
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Find the lengths of the medians of the triangle with vertices A (0, 0, 6), B (0, 4, 0) and (6, 0, 0).
Concept: undefined >> undefined
Find the coordinates of a point on y-axis which are at a distance of `5sqrt2` from the point P (3, –2, 5).
Concept: undefined >> undefined
A point R with x-coordinate 4 lies on the line segment joining the pointsP (2, –3, 4) and Q (8, 0, 10). Find the coordinates of the point R.
[Hint suppose R divides PQ in the ratio k: 1. The coordinates of the point R are given by `((8k + 2)/(k+1), (-3)/(k+1), (10k + 4)/(k+1))`
Concept: undefined >> undefined
