A sequence is said to be _____
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Two pairs of straight lines have the equations y2+xy−12x2=0 and ax2+2hxy+by2=0 . One line will be common among them if. (a)a+8h−16b=0 (b) a−8h+16b=0
(c)a−6h+9b=0 (d) a+6h+9b=0
Find the distance between parallel lines(i) 15x+8y34=0and 15x+8y+31=0(ii) l(x+y)+p=0l(x+y)−r=0.
If two lines represented by x4+x3y+cx2y2−xy3+y4=0 bisect the angle between the other two, then the value of c is (a) 0 (b) −1 (c) 1 (d) −6
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.
If the lines 2a+y3=0, 5x+ky3=0and 3xy2=0are concurrent, find the value of k.
Find the point of intersection of the pair of straight lines represented by the equation 6x2+5xy−21y2+13x+38y−5=0.
Find what the following equations become when the origin is shifted to the point (1, 1)(i) x2+xy−3y2−y+2=0(ii) xy−y2−x+y=0(iii) xy−x−y+1=0
Reduce the following equations into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive xaxis.(i) x−3y+8=0, (ii) y2=0, (iii) xy=4.