Consider a curve `ax^2+2hxy+by^2=1` and a point P not on the curve. A line drawn from the point P intersect the curve at points Q and R. If he product `PQ.PR` is (A) a pair of straight line (B) a circle (C) a parabola (D) an ellipse or hyperbola

The locus of the points of trisection of the double ordinates of the parabola y^2 = 4ax is : (A) a straight line (B) a circle (C) a parabola (D) none of these

The curve described parametrically by x=t^2+t+1 , and y=t^2-t+1 represents. (a) a pair of straight lines (b) an ellipse (c) a parabola (d) a hyperbola

The curve represented by the equation sqrt(p x)+sqrt(q y)=1 where p ,q in R ,p ,q >0, is (a) a circle (b) a parabola (c) an ellipse (d) a hyperbola

The locus of the points of trisection of the double ordinates of a parabola is a a. pair of lines b. circle c. parabola d. straight line

A tangent to the parabola x^2 =4ay meets the hyperbola xy = c^2 in two points P and Q. Then the midpoint of PQ lies on (A) a parabola (C) a hyperbola (B) an ellipse (D) a circle

Normal at 3 points P, Q, and R on a rectangular hyperbola intersect at a point on a curve the centroid of triangle PQR

Prove that the locus of the point of intersection of the normals at the ends of a system of parallel cords of a parabola is a straight line which is a normal to the curve.

A given line L_1 cut x and y-axes at P and Q respectively and has intercepts a and b/2 on x and y-axes respectively. Let another line L_2 perpendicular to L_1 cut x and y-axes at R and S respectively. Let T be the point of intersection of PS and QR . A straight line passes through the centre of locus of T . Then locus of the foot of perpendicular to it from origin is : (A) a straight line (B) a circle (C) a parabola (D) none of these

In DeltaPQR,Pq=PR and S is the mid-point of PQ. A line drawn from S parallel to QR, intersects the line PR at T. Prove that PS = PT.

Find the product of the perpendiculars drawn from the point (x_1,y_1) on the lines ax^2+2hxy+by^2=0