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The equations of two sides of a square are 5x − 12y − 65 = 0 and 5x − 12y + 26 = 0. Find the area of the square.
Concept: undefined >> undefined
Find the equation of two straight lines which are parallel to x + 7y + 2 = 0 and at unit distance from the point (1, −1).
Answer 3:
Concept: undefined >> undefined
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Prove that the lines 2x + 3y = 19 and 2x + 3y + 7 = 0 are equidistant from the line 2x + 3y= 6.
Concept: undefined >> undefined
Find the ratio in which the line 3x + 4y + 2 = 0 divides the distance between the line 3x + 4y + 5 = 0 and 3x + 4y − 5 = 0
Concept: undefined >> undefined
Find the equations of the lines through the point of intersection of the lines x − y + 1 = 0 and 2x − 3y+ 5 = 0, whose distance from the point(3, 2) is 7/5.
Concept: undefined >> undefined
If the centroid of a triangle formed by the points (0, 0), (cos θ, sin θ) and (sin θ, − cos θ) lies on the line y = 2x, then write the value of tan θ.
Concept: undefined >> undefined
Write the value of θ ϵ \[\left( 0, \frac{\pi}{2} \right)\] for which area of the triangle formed by points O (0, 0), A (a cos θ, b sin θ) and B (a cos θ, − b sin θ) is maximum.
Concept: undefined >> undefined
Write the distance between the lines 4x + 3y − 11 = 0 and 8x + 6y − 15 = 0.
Concept: undefined >> undefined
If the lines x + ay + a = 0, bx + y + b = 0 and cx + cy + 1 = 0 are concurrent, then write the value of 2abc − ab − bc − ca.
Concept: undefined >> undefined
Write the locus of a point the sum of whose distances from the coordinates axes is unity.
Concept: undefined >> undefined
L is a variable line such that the algebraic sum of the distances of the points (1, 1), (2, 0) and (0, 2) from the line is equal to zero. The line L will always pass through
Concept: undefined >> undefined
The distance between the orthocentre and circumcentre of the triangle with vertices (1, 2), (2, 1) and \[\left( \frac{3 + \sqrt{3}}{2}, \frac{3 + \sqrt{3}}{2} \right)\] is
Concept: undefined >> undefined
Area of the triangle formed by the points \[\left( (a + 3)(a + 4), a + 3 \right), \left( (a + 2)(a + 3), (a + 2) \right) \text { and } \left( (a + 1)(a + 2), (a + 1) \right)\]
Concept: undefined >> undefined
The line segment joining the points (−3, −4) and (1, −2) is divided by y-axis in the ratio
Concept: undefined >> undefined
The area of a triangle with vertices at (−4, −1), (1, 2) and (4, −3) is
Concept: undefined >> undefined
The line segment joining the points (1, 2) and (−2, 1) is divided by the line 3x + 4y = 7 in the ratio ______.
Concept: undefined >> undefined
Distance between the lines 5x + 3y − 7 = 0 and 15x + 9y + 14 = 0 is
Concept: undefined >> undefined
The value of λ for which the lines 3x + 4y = 5, 5x + 4y = 4 and λx + 4y = 6 meet at a point is
Concept: undefined >> undefined
The vertices of a triangle are (6, 0), (0, 6) and (6, 6). The distance between its circumcentre and centroid is
Concept: undefined >> undefined
The ratio in which the line 3x + 4y + 2 = 0 divides the distance between the line 3x + 4y + 5 = 0 and 3x + 4y − 5 = 0 is
Concept: undefined >> undefined
