If the lines ax2 + 2xy + by2 = 0 meet the line px + qy = pq in points which are equidistant fromthe origin, prove that h(p? - q?) = pq(a - b).

The straight line ax + by = 1 makes with the curve px^2 + 2axy + qy^2 = r , a chord which subtends aright angle at the origin. Then

If the line px + qy =1 is a tangent to the parabola y^(2) =4ax, then

If r is the geometric mean of p and q, then the line px+qy+r=0

If the line px+qy=1 is a tangent to the parabola y^(2)=4ax. then

The straight line px+qy=1 makes the ax^2+2hxy+by^2=c , a chord which subtends a right angle at the origin . Show that c(p^2+q^2) =a+b . Also show that px+qy=1 touches a circle whose radius is sqrt(c/(a+b))

The straight line px+qy=1 makes the ax^2+2hxy+by^2=c , a chord which subtends a right angle at the origin . Show that c(p^2+q^2) =a+b . Also show that px+qy=1 touches a circle whose radius is sqrt(c/(a+b))

If the slope of one of the line given by 2px^(2)-16xy+qy^(2)=0 is 2, then the equation of the other line, is