Perpendicular Form of a Straight Line
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The line passes through and makes an angle of ___ with the-axis.
Let and be the slopes of three-line segments , respectively, where is the origin. If the circumcentre of the coincides with the origin and its orthocentre lies on the then the value of is equal to
If is angle between the curves and , then is equal to
The angle between the curves and at the point is
- √3 x+y=6
- √3 x−y=6
- x−√3 y=6
- x+√3 y=6
The length of the perpendicular from the origin to a line is 7 and the perpendicular makes an angle of 150∘ with the positive direction of the x-axis. Find the equation of the line.
√3x+y−14=0
√3x−y−14=0
−√3x−y−14=0
−√3x+y−14=0
- y(cosα+sinα)+x(sinα−cosα)=a
- y(cosα+sinα)+x(sinα+cosα)=a
- y(cosα+sinα)+x(cosα−sinα)=a
- y(cosα−sinα)−x(sinα−cosα)=a
The sum of a two-digit number and the number formed by reversing the digits is 33. Also the sum of the digits is 4.Represent the above situation algebraically and graphically.
True
False
- (√3+1)x+(√3−1)y=8√2
- (√3−1)x+(√3+1)y=8√2
- √3x+y=8
- x+√3y=8
- 3√13x+2√13y=12√13
- 12√13x+13√13y=2√13
- y=−32x+6
- 3x+2y=12
- 3x−2y+1=0
- 3x−2y=2
- 3x−2y=1
- 3x−2y+2=0
If the circles x2+y2+2ax+cy+a=0andx2+y2−3ax+dy−1=0 interesect in two distinct points P andn Q then the line 5x + by - a = 0 passes through P and Q for
(2005)
exactly two value of a
exactly on value of a
no value of a
infinitely many values of
True
False
Let the algebric sum of the perpendicular distances from the points (2, 0), (0, 2), (1, 1) to a variable straight line be zero, then the line passes through a fixed point whose co-ordinates are
(I.I.T 1991)
(2, 2)
(0, 0)
none
(1, 1)
The perpendicular distance from (1, 2) to the straight line 12x+5y=7 is
1513
1213
513
713
(where M1>M2)