If the lines `L_1` and `L_2` are tangents to `4x^2-4x-24 y+49=0` and are normals for `x^2+y^2=72 ,` then find the slopes of `L_1` and `L_2dot`

If the lines L_1a n dL_2 are tangents to 4x^2-4x-24 y+49=0 and are normals for x^2+y^2=72 , then find the slopes of L_1 and L_2dot

The combined equation of the lines L_(1) and L_(2) is 2x^(2)+6xy+y^(2)=0 and that lines L_(3) and L_(4) is 4x^(2)+18xy+y^(2)=0 . If the angle between L_(1) and L_(4) be alpha , then the angle between L_(2) and L_(3) will be

Two lines L_(1) and L_(2) of slops 1 are tangents to y^(2)=4x and x^(2)+2y^(2)=4 respectively, such that the distance d units between L_(1) and L _(2) is minimum, then the value of d is equal to

The combined equation of the lines l_1a n dl_2 is 2x^2+6x y+y^2=0 and that of the lines m_1a n dm_2 is 4x^2+18 x y+y^2=0 . If the angle between l_1 and m_2 is alpha then the angle between l_2a n dm_1 will be

The combined equation of the lines l_1a n dl_2 is 2x^2+6x y+y^2=0 and that of the lines m_1a n dm_2 is 4x^2+18 x y+y^2=0 . If the angle between l_1 and m_2 is alpha then the angle between l_2a n dm_1 will be

Find the equation of tangents to hyperbola x^(2)-y^(2)-4x-2y=0 having slope 2.

Let l_(1) and l_(2) be the two lines which are normal to y^(2)=4x and tangent to x^(2)=-12y respectively (where, l_(1) and l_(2) are not the x - axis). Then, the product of the slopes of l_(1)and l_(2) is

Let the lines l_(1) and l_(2) be normals to y^(2)=4x and tangents to x^(2)=-12y (where l_(1) and l_(2) are not x - axis). The absolute value of the difference of slopes of l_(1) and l_(2) is

The bisector of two lines L and L are given by 3x^2 - 8xy - 3y^2 + 10x + 20y - 25 = 0 . If the line L_1 passes through origin, find the equation of line L_2 .

Let two parallel lines L_1 and L_2 with positive slope are tangent to the circle C_1 : x^2 + y^2 -2x 16y + 64 = 0 . If L_1 is also tangent to the circle C_2 : x^2 + y^2 - 2x + 2y -2 = 0 and the equation of L_2 is asqrta x - by + c - a sqrta = 0 where a,b,c in N. then find the value of (a+b+c)/7