Home
Class 11
MATHS
The condition that one of the straight l...

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)`

Promotional Banner

Similar Questions

Explore conceptually related problems

If the equations x^2+p x+q=0a n dx^2+p^(prime)x+q^(prime)=0 have a common root, then it must be equal to a. (p^(prime)-p ^(prime) q)/(q-q^(prime)) b. (q-q ')/(p^(prime)-p) c. (p^(prime)-p)/(q-q^(prime)) d. (p q^(prime)-p^(prime) q)/(p-p^(prime))

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

Using determinants prove that the points (a ,\ b),\ (a^(prime),\ b^(prime))a n d\ (a-a^(prime),\ b-b^(prime)) are collinear if a b^(prime)=a^(prime)bdot

|(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

If a function is represented parametrically be the equations x=(1+(log)_e t)/(t^2); y=(3+2(log)_e t)/t , then which of the following statements are true? (a) y^('')(x-2x y^(prime))=y (b) y y^(prime)=2x(y^(prime))^2+1 (c) x y^(prime)=2y(y^(prime))^2+2 (d) y^('')(y-4x y^(prime))=(y^(prime))^2

If the normal to the given hyperbola at the point (c t , c/t) meets the curve again at (c t^(prime), c/t^(prime)), then (A) t^3t^(prime)=1 (B) t^3t^(prime)=-1 (C) t t^(prime)=1 (D) t t^(prime)=-1

If x^2+y^2=1,t h e n (a) y y^('')-2(y^(prime))^2+1=0 (b) yy^('')+(y^(prime))^2+1=0 (c) y y^('')+(y^(prime))^(-2)-1=0 (d) y y^('')+2(y^(prime))^2+1=0

If the abscissae and the ordinates of two point Aa n dB be the roots of a x^2+b x+c=0a n da^(prime)y^2+b^(prime)y=c^(prime)=0 respectively, show that the equation of the circle described on A B as diameter is a a^(prime)(x^2+y^2)+a^(prime)b x+a b^(prime)y+(c a^(prime)+ca)=0.

The sum of the exponents of the prime factors in the prime factorisation of 196, is (a) 1 (b) 2 (c) 4 (d) 6

The product of any natural number and the smallest prime is an even number (b) an odd number a prime number (d) None of these