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 pair of lines joining origin to the points of intersection of, the two curves ax^2+2hxy + by^2+2gx = 0 and a^'x^2 +2h^'xy + b^'y^2 + 2g^'x = 0 will be at right angles, if

The lines joining the origin to the points of intersection of the line 3x-2y -1 and the curve 3x^2 + 5xy -3y^2+2x +3y= 0 , are

If the straight lines joining origin to the points of intersection of the line x+y=1 with the curve x^2+y^2 +x-2y -m =0 are perpendicular to each other , then the value of m should be

The lines joining the origin to the point of intersection of The lines joining the origin to the point of intersection of 3x^2+m x y=4x+1=0 and 2x+y-1=0 are at right angles. Then which of the following is not a possible value of m ? -4 (b) 4 (c) 7 (d) 3

If the lines joining the points of intersection of the curve 4x^2+9y+18 x y=1 and the line y=2x+c to the origin are equally inclined to the y-axis, the c is: -1 (b) 1/3 (c) 2/3 (d) -1/2

If the lines joining the points of intersection of the curve 4x^2+9y+18 x y=1 and the line y=2x+c to the origin are equally inclined to the y-axis, the c is: -1 (b) 1/3 (c) 2/3 (d) -1/2

Find the equation of the normal to the curve x^2/a^2-y^2/b^2=1 at (x_0,y_0)

Two conics a_1x^2+2h_1xy + b_1y^2 = c_1, a_2x^2 + 2h_2xy+b_2y^2 = c_2 intersect in 4 concyclic points. Then

Find the condition for the two concentric ellipses a_1x^2+\ b_1y^2=1\ a n d\ a_2x^2+\ b_2y^2=1 to intersect orthogonally.

(1) The straight lines (2k+3) x + (2-k) y+3=0 , where k is a variable, pass through the fixed point (-3/7, -6/7) . (2) The family of lines a_1 x+ b_1 y+ c_1 + k (a_2 x + b_2 y + c_2) = 0 , where k is a variable, passes through the point of intersection of lines a_1 x + b_1 y + c_1 = 0 and a_2 x+ b_2 y + c_2 = 0 (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not a correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true