If the quadrilateral formed by the lines `a x+b y+c=0,a^(prime)x+b^(prime)y+c=0,a x+b y+c^(prime)=0,a^(prime)x+b^(prime)y+c^(prime)=0` has perpendicular diagonals, then (a) `b^2+c^2=b^('2)+c^('2)` (b)`c^2+a^2=c^('2)+a^('2)` (c)`a^2+b^2=a^('2)+b^('2)` (d) none of these

the diagonals of the parallelogram formed by the the lines a_(1)x+b_(1)y+c_(1)=0,a_(1)x+b_(1)y+c_(1)^(prime)=0,a_(2)x+b_(2)y+c_(1)=0,a_(2)x+b_(2)y+c_(1)^(prime) will be right angles if:

|(bc,bcprime+bprime c, bprime c prime),(ca,ca prime+c prime a,c prime a prime),(ab, ab prime+a prime b,a prime b prime)| is equal to

The angle between the lines a _(1) x + b_(1)y+c_(1) =0 and a _(2)x+ b_(2)y+c_(2)=o, is

The condition that one of the straight lines given by the equation a x^2+2h x y+b y^2=0 may coincide with one of those given by the equation a^(prime)x^2+2h^(prime)x y+b^(prime)y^2=0 is (a b^(prime)-a^(prime)b)^2=4(h a^(prime)-h^(prime)a)(b h^(prime)-b^(prime)h) (a b^(prime)-a^(prime)b)^2=(h a^(prime)-h^(prime)a)(b h^(prime)-b^(prime)h) (h a^(prime)-h^(prime)a)^2=4(a b^(prime)-a^(prime)b)(b h^(prime)-b^(prime)h) (b h^(prime)-b^(prime)h)^2=4(a b^(prime)-a^(prime)b)(h a^(prime)-h^(prime)a)

Show the condition that the curves a x^2+b y^2=1 and a^(prime)\ x^2+b^(prime)\ y^2=1 Should intersect orthogonally

Two systems of rectangular axes have the same origin. If a plane cuts them at distances a ,b ,ca n da^(prime),b^(prime),c^(prime) respectively, prove that 1/(a^2)+1/(b^2)+1/(c^2)=1/(a^('2))+1/(b^('2))+1/(c^('2))

The differential equation of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=C is a. y^(primeprime)/y^(prime)+y^(prime)/y-1/x=0 b. y^(primeprime)/y^(prime)+y^(prime)/y+1/x=0 c. y^(primeprime)/y^(prime)-y^(prime)/y-1/x=0 d. none of these

The least prime number is 0 (b) 1 (c) 2 (d) 3