`2x^(2)+5xy+3y^(2)+6x+7y+4=0` represents two lines `y=m_(1)x+c_(1)` and `y=m_(2)x+c_(2)` then `m_(1)+m_(2)` and `m_(1)times m_(2)` are

If the equation ax^(2)+2hxy+by^(2)=0 represented two lines y=m_(1)x and y=m_(2)x the

If y+b=m_(1)(x+a) and y+b=m_(2)(x+a) are two tangents to y^(2)=4ax then m_(1)times m_(2)=

STATEMENT-1: The straight lines 2x+3y+5=0and 3x-2y+1=0 are perpendicular to each other. STATEMENT-2: Two lines y=m_(1)x+c_(1)and y=m_(2)x+c_(2) where m_(1),m_(2)in R are perpendicular if m_(1),m_(2)=-1. STATEMENT-2: Two lines y=m_(1)xx+x_(1)and y=m_(2)x+c_(2)where m_(1),m_(2)inR are peprendicular if m_(1)m_(2)=-1.

Show that the area of the triangle formed by the lines y=m_(1)x+c_(1),y=m_(2)x+c_(2) and and is 2|m_(1)-m_(2)|

(i) Find the value of 'a' if the lines 3x-2y+8=0 , 2x+y+3=0 and ax+3y+11=0 are concurrent. (ii) If the lines y=m_(1)x+c_(1) , y=m_(2)x+c_(2) and y=m_(3)x+c_(3) meet at point then shown that : c_(1)(m_(2)-m_(3))+c_(2)(m_(3)-m_(1))+c_(3)(m_(1)-m_(2))=0

Find the coordinates that the straight lines y=m_(1)x+c_(1),y=m_(2)x+c_(2) and y=m_(2)x+c_(3) may meet in a point.

Two straight lines (y-b)=m_(1)(x+a) and (y-b)=m_(2)(x+a) are the tangents of y^(2)=4ax. Prove m_(1)m_(2)=-1

If x_(1), x_(2), x_(3) are the abcissa of the points A_(1), A_(2), A_(3) respectively where the lines y=m_(1)x, y=m_(2)x, y =m_(3) x meet the line 2x-y+3=0 such that m_(1),m_(2),m_(3) are in A.P., then x_(1),x_(2),x_(3) are in

Find the point of intersection of the following pairs of lines: y=m_(1)x+(a)/(m_(1)) and y=m_(2)x+(a)/(m_(2))