Find the condition for the line y= mx to cut at right angles the conic `ax^(2)+2hxy+by^(2)=1.`

Find the condition for the line y=m x to cut at right angles the conic a x^2+2h x y+b y^2=1.

Find the condition for the line y=mx+c to be a tangent to the parabola x^(2)=4ay .

Find the condition for the line y=mx+c to be a tangent to the parabola x^(2)=4ay .

The lines y = mx bisects the angle between the lines ax^(2) +2hxy +by^(2) = 0 if

Find the condition that the straight line y = mx + c touches the hyperbola x^(2) - y^(2) = a^(2) .

Find the conditions that the line (i) y = mx + c may touch the circle x^(2) +y^(2) = a^(2) , (ii) y = mx + c may touch the circle x^(2) + y^(2) + 2gx + 2fy + c = 0 .

Find the points in which the line y = 2x + 1 cuts the circle x^(2) + y^(2) = 2 .

Statement-I : The condition for the line y = mx+c to be a tangent to (x+a)^(2) = 4ay is c = am(1-m). Statement-II : The condition for tbe line y = mx + c to be a focal chord to y^(2) = 4ax is c+am=0 Statement-III : The condition for the line y = mx + c to be a tangent x^(2)=4ay is c = - am^(2) Which of above stattements is true

The condition that the line y=mx+c may be a tangent to (y^(2))/(a^(2))-x^(2)/b^(2)=1 is

The condition that one of the straight lines given by the equation ax^(2)+2hxy+by^(2)=0 may coincide with one of those given by the equation a'x^(2)+2h'xy+b'y^(2)=0 is