Two lines are drawn at right angles, one being a tangent to `y^2=4a x` and the other `x^2=4b ydot` Then find the locus of their point of intersection.

Find the equation of the common tangent of y^2=4a x and x^2=4a ydot

If the tangents to the parabola y^2=4a x intersect the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at Aa n dB , then find the locus of the point of intersection of the tangents at Aa n dBdot

If the chord of contact of tangents from a point P to the parabola y^2=4a x touches the parabola x^2=4b y , then find the locus of Pdot

Tangents are drawn from any point on the hyperbola (x^2)/9-(y^2)/4=1 to the circle x^2+y^2=9 . Find the locus of the midpoint of the chord of contact.

Two straight lines are perpendicular to each other. One of them touches the parabola y^2=4a(x+a) and the other touches y^2=4b(x+b) . Their point of intersection lies on the line. (a) x-a+b=0 (b) x+a-b=0 (c) x+a+b=0 (d) x-a-b=0

If O is origin and R is a variable point on y^2=4x , then find the equation of the locus of the mid-point of the line segmet OR .

If O is origin and R is a variable point on y^(2)=4x , then find the equation of the locus of the mid-point of the line segment OR.

Tangents are drawn to the parabola y^2=4a x at the point where the line l x+m y+n=0 meets this parabola. Find the point of intersection of these tangents.

Given x/a+y/b=1 and ax + by =1 are two variable lines, 'a' and 'b' being the parameters connected by the relation a^2 + b^2 = ab . The locus of the point of intersection has the equation