Intercept of a Straight Line
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Q. Match List I with the List II and select the correct answer using the code given below the lists :
Let the line L:ax+by+c=0 intersect x−axis at A and y−axis at B. Let O be the origin.
List IList II(I)If a, b, c are in G.P. with common ratio as 2, then area of ΔAOB is(P)6(II)If a=1, b=1, c=2 and circumradius of ΔAOB is √p, p>0, then the value of 3p is(Q)4(III)If a=b=c=1 and reflection of O along the line L is (α, β), then |α+β| is (R)2(IV)If a=b=1, c=√2 and d is the shortest distance of line L from O, then 2d is (S)3(T)1
Which of the following is CORRECT combination?
Let the line L:ax+by+c=0 intersect x−axis at A and y−axis at B. Let O be the origin.
List IList II(I)If a, b, c are in G.P. with common ratio as 2, then area of ΔAOB is(P)6(II)If a=1, b=1, c=2 and circumradius of ΔAOB is √p, p>0, then the value of 3p is(Q)4(III)If a=b=c=1 and reflection of O along the line L is (α, β), then |α+β| is (R)2(IV)If a=b=1, c=√2 and d is the shortest distance of line L from O, then 2d is (S)3(T)1
Which of the following is CORRECT combination?
- (I)→(R); (II)→(S); (III)→(Q); (IV)→(P)
- (I)→(Q); (II)→(T); (III)→(P) (IV)→(R)
- (I)→(Q); (II)→(T); (III)→(S); (IV)→(R)
- (I)→(Q); (II)→(P); (III)→(R); (IV)→(R)
Q.
ax + by = ab is the equation of a straight line which makes intercepts a & b on x & y axis respectively. State True or False.
True
False
Q. The area of triangle formed by the lines x = 0, y = 0 and xa+yb=1, a and b are positive , is
Q. Slope of a line which cuts intercepts of equal lengths on the axes is
- 2
- 0
- −1
- √3
Q. The equation of the straight line which passes through the point (1, - 2) and cuts off equal intercepts from axes, is
- x+y=1
- x-y=1
- x+y+1=0
- x-y-2=0
Q. A straight line through origin O meets the lines 3y=10−4x and 8x+6y+5=0 at points A and B respectively. Then O divides the segment AB in the ratio:
- 4:1
- 3:4
- 2:3
- 1:2
Q. The area enclosed by 2|x|+3|y|≤6 is
- 3 sq. units
- 4 sq. units
- 12 sq. units
- 24 sq. units
Q. If a line parallel to 2x+6y−7=0 makes an intercept of 10 units between the coordinate axes and y− intercept is ±√k, then the value of k is
Q. The equation of line passing through (3, 4) and parallel to 5x+9y+12=0 is
- 5x−9y+51=0
- 5x−9y−51=0
- 5x+9y+51=0
- 5x+9y−51=0
Q. The area (in sq. units) of the triangle formed by the coordinate axes and the line x(tanθ)+y(cotθ)=4 where θ∈(0, π2), is