The equation `a^2x^2+2h(a+b)x y+b^2y^2=0` and `a x^2+2h x y+b y^2=0` represent

Two pairs of straight lines have the equations y^2+x y-12 x^2=0 and a x^2+2h x y+b y^2=0 . One line will be common among them if. a+8h-16 b=0 (b) a-8h+16 b=0 a-6h+9b=0 (d) a+6h+9b=0

If the lines joining the origin and the point of intersection of curves a x^2+2h x y+b y^2+2gx+0 and a_1x^2+2h_1x y+b_1y^2+2g_1x=0 are mutually perpendicular, then prove that g(a_1+b_1)=g_1(a+b)dot

The image of the pair of lines represented by a x^2+2h x y+b y^2=0 by the line mirror y=0 is a. a x^2-2h x y-b y^2=0 b. b x^2-2h x y+a y^2=0 c. x^2+2h x y+a y^2=0 d. a x^2-2h x y+b y^2=0

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)

The equation sin^2theta=(x^2+y^2)/(2x y),x , y!=0 is possible if

The equation x^(2)y^(2)-9y^(2)-6x^(2)y+54y=0 represents

Find the condition if the circle whose equations are x^2+y^2+c^2=2a x and x^2+y^2+c^2-2b y=0 touch one another externally.

If the conics whose equations are S-=sin^2thetax^2+2h x y+cos^2thetay^2+32 x+16 y+19=0,S^(prime)-=cos^2thetax^2+ 2h^(prime)x y+sin^2thetay^2+16 x+32y+19=0 intersect at four concyclic points, then, (where theta in R) (a) h+h^(prime)=0 (b) h=h ' (c) h+h^(prime)=1 (d) none of these

A tangent at a point on the circle x^2+y^2=a^2 intersects a concentric circle C at two points Pa n dQ . The tangents to the circle X at Pa n dQ meet at a point on the circle x^2+y^2=b^2dot Then the equation of the circle is (a) x^2+y^2=a b (b) x^2+y^2=(a-b)^2 (c) x^2+y^2=(a+b)^2 (d) x^2+y^2=a^2+b^2

Statement 1 : If -2h=a+b , then one line of the pair of lines a x^2+2h x y+b y^2=0 bisects the angle between the coordinate axes in the positive quadrant. Statement 2 : If a x+y(2h+a)=0 is a factor of a x^2+2h x y+b y^2=0, then b+2h+a=0 .