Show that the four lines `ax pm by pm c = 0 ` enclose a rhombus whose area is `(2c^(2))/(|ab|)`

Area of the rhombus bounded by the four lines, ax +- by +-c = 0 is

Show that the area enclosed by y^(2)=4ax and its latus rectum is (8a^(2))/(3) sq units.

(i) If a, b, c, are in A.P. then show that ax….+….by +c=0 passes through a fixed point. Find then fixed point. (ii) If 9a^(2)+16b^(2)-24ab-25c^(2)=0, then the family of straight lines ax+by+0 is concurrent at the point whose co-ordinates are given by "________" (iii) If 3a+4b-5c=0, then the family of straight lines ax+by+c=0 passes through a fixed point. Find the coordinates of the point.

If a^2+b^2-c^2-2ab = 0 , then the family of straight lines ax + by + c = 0 is concurrent at the points

Show that the distance between the parallel lines ax+by+c=0 and k(ax+by)+d=0 is |(c-(d)/(k))/(sqrt(a^(2)+b^(2)))|

The equation of the hyperbola whose foci are (pm5,0) and length of the latus rectum is (9)/(2) is

Show that the points A (1, 0), B(5, 3), C (2, 7) and D(-2, 4) are the vertices of a rhombus.

Show that the equation to the parallel line mid-way between the parallel lines ax+by+c_(1)=0andax+by+c_(2)=0 is ax+by+(c_(1)+c_(2))/2=0

For a hyperbola, the foci are at (pm 4, 0) and vertices at (pm 2 , 0) . Its equation is

Show that the area of a rhombus is half the product of the lengths of its diagonals. GIVEN : A rhombus A B C D whose diagonals A C and B D intersect at Odot TO PROVE : a r(r hom b u sA B C D)=1/2(A C*B D)