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Find the measure of the acute angle between the line represented by `3"x"^2 - 4sqrt3"xy" + 3"y"^2 = 0`
Concept: undefined >> undefined
Find the measure of the acute angle between the line represented by:
2x2 + 7xy + 3y2 = 0
Concept: undefined >> undefined
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Find the measure of the acute angle between the line represented by:
4x2 + 5xy + y2 = 0
Concept: undefined >> undefined
Find the measure of the acute angle between the line represented by:
(a2 - 3b2)x2 + 8abxy + (b2 - 3a2)y2 = 0
Concept: undefined >> undefined
Find the combined equation of lines passing through the origin each of which making an angle of 30° with the line 3x + 2y - 11 = 0
Concept: undefined >> undefined
If the angle between the lines represented by ax2 + 2hxy + by2 = 0 is equal to the angle between the lines 2x2 - 5xy + 3y2 = 0, then show that 100 (h2 - ab) = (a + b)2.
Concept: undefined >> undefined
Find the combined equation of lines passing through the origin and each of which making an angle of 60° with the Y-axis.
Concept: undefined >> undefined
Choose correct alternatives:
If acute angle between lines ax2 + 2hxy + by2 = 0 is, `pi/4`, then 4h2 = ______.
Concept: undefined >> undefined
Find the joint equation of the pair of lines which bisect angles between the lines given by x2 + 3xy + 2y2 = 0
Concept: undefined >> undefined
If the slope of one of the lines given by ax2 + 2hxy + by2 = 0 is three times the other, prove that 3h2 = 4ab.
Concept: undefined >> undefined
Show that the line 3x + 4y + 5 = 0 and the lines (3x + 4y)2 - 3(4x - 3y)2 = 0 form the sides of an equilateral triangle.
Concept: undefined >> undefined
Show that the lines x2 - 4xy + y2 = 0 and the line x + y = `sqrt6` form an equilateral triangle. Find its area and perimeter.
Concept: undefined >> undefined
If the slope of one of the lines given by ax2 + 2hxy + by2 = 0 is square of the slope of the other line, show that a2b + ab2 + 8h3 = 6abh.
Concept: undefined >> undefined
Prove that the product of length of perpendiculars drawn from P(x1, y1) to the lines represented by ax2 + 2hxy + by2 = 0 is `|("ax"_1^2 + "2hx"_1"y"_1 + "by"_1^2)/(sqrt("a - b")^2 + "4h"^2)|`
Concept: undefined >> undefined
Show that the difference between the slopes of the lines given by (tan2θ + cos2θ)x2 − 2xy tan θ + (sin2θ)y2 = 0 is two.
Concept: undefined >> undefined
A table of values of f, g, f' and g' is given :
| x | f(x) | g(x) | f'(x) | g'(x) |
| 2 | 1 | 6 | –3 | 4 |
| 4 | 3 | 4 | 5 | -6 |
| 6 | 5 | 2 | –4 | 7 |
If r(x) =f [g(x)] find r' (2).
Concept: undefined >> undefined
A table of values of f, g, f' and g' is given :
| x | f(x) | g(x) | f'(x) | g'(x) |
| 2 | 1 | 6 | –3 | 4 |
| 4 | 3 | 4 | 5 | -6 |
| 6 | 5 | 2 | –4 | 7 |
If R(x) =g[3 + f(x)] find R'(4).
Concept: undefined >> undefined
A table of values of f, g, f' and g' is given:
| x | f(x) | g(x) | f'(x) | g'(x) |
| 2 | 1 | 6 | –3 | 4 |
| 4 | 3 | 4 | 5 | –6 |
| 6 | 5 | 2 | –4 | 7 |
If s(x) = f[9 − f (x)] find s'(4).
Concept: undefined >> undefined
A table of values of f, g, f' and g' is given :
| x | f(x) | g(x) | f'(x) | g'(x) |
| 2 | 1 | 6 | –3 | 4 |
| 4 | 3 | 4 | 5 | -6 |
| 6 | 5 | 2 | –4 | 7 |
If S(x) =g [g(x)] find S'(6).
Concept: undefined >> undefined
Assume that `f'(3) = -1,"g"'(2) = 5, "g"(2) = 3 and y = f["g"(x)], "then" ["dy"/"dx"]_(x = 2) = ?`
Concept: undefined >> undefined
