In a certain sequence of 8 numbers, each number after the first is 1 more than the previous number .If the first number is -5, how many of the numbers in the sequence are positive?
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Show that the area of the triangle formed by the lines y=m1x+c1,y=m2x+c2and x=0is 2∣m1−m2∣(c1−c2)2
Find the equation of the line passing through the point of intersection of the lines 4x+7y−3=0and 2x−3y+1=0that has equal intercepts on the axes.
The vertices of Δ PQR are P(2,1), Q(2,3)and R(4,5). Find equation of the median through the vertex R.
If the equation of the pair of straight lines passing through the point (1,1)
, one making an angle θ
with the positive direction of the x-axis and the other making the same angle with the positive direction of the y-axis, is x2−(a+2)xy+y2+a(x+y−1)=0,a=2,
then the value of sin2θ
Statement 1 : If −2h=a+b, then one line of the pair of lines ax2+2hxy+by2=0 bisects the angle between the coordinate axes in the positive quadrant. Statement 2 : If ax+y(2h+a)=0 is a factor of ax2+2hxy+by2=0, then b+2h+a=0
Both the statements are true but statement 2 is the correct explanation of statement 1. Both the statements are true but statement 2 is not the correct explanation of statement 1. Statement 1 is true and statement 2 is false. Statement 1 is false and statement 2 is true.
A line L
passing through the point (2, 1) intersects the curve 4x2+y2−x+4y−2=0
at the point AandB
. If the lines joining the origin and the points A,B
are such that the coordinate axes are the bisectors between them, then find the equation of line L˙
Find the distance between the pair of parallel lines x2+4xy+4y2+3x+6y−4=0
Find the angle between the lines represented by x2+2xysecθ+y2=0