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Find the joint equation of the pair of lines which pass through the origin and are perpendicular to the lines represented the equation y2+3xy−6x+5y−14=0
Find the equation of the line through the intersection of 5x−3y=1and 2x−3y−23=0and perpendicular to the line 5x−3y−1=0.
If the equation x2+(λ+μ)xy+λuy2+x+μy=0
represents two parallel straight lines, then prove that λ=μ˙
If the pairs of lines x2+2xy+ay2=0 and ax2+2xy+y2=0 have exactly one line in common, then the joint equation of the other two lines is given by (1) 3x2+8xy−3y2=0
Find the equation of the line which satisfy the given conditions : Passing through the point (−4,3)with slope 21.
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 area of the triangle formed by the lines y−x=0,x+y=0and x−k=0.
x+y=7 and ax2+2hxy+ay2=0,(a=0) , are three real distinct lines forming a triangle. Then the triangle is (a) isosceles (b) scalene equilateral (d) right angled