`l_1` is the tangent to `2x^2+3 y^2 =35` at (4,-1) & `l_2` is the tangent to `4 x^2 + y^2 =25` at(2,-3). The distance between `l_1 and l_2` is

Let L_1 be a tangent to the parabola y^(2) = 4(x+1) and L_2 be a tangent to the parabola y^(2) = 8(x+2) such that L_1 and L_2 intersect at right angles. Then L_1 and L_2 meet on the straight line :

Consider two lines L_1:2x+y=4 and L_2:(2x-y=2) .Find the angle between L1 and L2 .

Two lines L_(1) and L_(2) of slops 1 are tangents to y^(2)=4x and x^(2)+2y6(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

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

Consider the lines L _(1) : (x +1)/( 3) = (y+2)/(1) = (z+1)/(2), L_(2): (x-2)/(1) = (y+2)/(2) = (z-3)/(3) The shortest distance between L _(1) and L _(2) is

The combined equation of the lines L_1 and L_2 is 2x^2+6xy+y^2=0 , and that of the 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_1 and L_3 will be .

The combined equation of the lines L_1 and L_2 is 2x^2+6xy+y^2=0 , and that of the 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 .

Let L be the line x-2y+3=0 .The equation of line L_1 is parallel to L and passing through (1,-2).Find the distance between L and L_1 .

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