The curve in the first quadrant for which the normal at any point `(x , y)` and the line joining the origin to that point form an isosceles triangle with the x-axis as base is (a) an ellipse (b) a rectangular hyperbola (c) a circle (d) None of these

Plot the region in the first quadrant in which points are nearer to the origin than to the line x=3.

The curve for which the length of the normal is equal to the length of the radius vector is/are (a) circles (b) rectangular hyperbola (c) ellipses (d) straight lines

A normal at any point (x , y) to the curve y=f(x) cuts a triangle of unit area with the axis, the differential equation of the curve is

The locus a point P(alpha,beta) moving under the condition that the line y=alphax+beta is a tangent to the hyperbola x^2/a^2-y^2/b^2=1 is (A) a parabola (B) an ellipse (C) a hyperbola (D) a circle

The equation of the locus of the middle point of a chord of the circle x^2+y^2=2(x+y) such that the pair of lines joining the origin to the point of intersection of the chord and the circle are equally inclined to the x-axis is x+y=2 (b) x-y=2 2x-y=1 (d) none of these

Find the area of the triangle formed by the tangents from the point (4, 3) to the circle x^2+y^2=9 and the line joining their points of contact.

Show that the angle between the tangent at any point P and the line joining P to the origin O is same at all points on the curve log(x^2+y^2)=ktan^(-1)(y/x)

With a given point and line as focus and directrix, a series of ellipses are described. The locus of the extremities of their minor axis is an (a)ellipse (b)a parabola (c)a hyperbola (d)none of these

The locus of a point whose chord of contact with respect to the circle x^2+y^2=4 is a tangent to the hyperbola x y=1 is a/an ellipse (b) circle hyperbola (d) parabola

The length of the transverse axis of the rectangular hyperbola x y=18 is 6 (b) 12 (c) 18 (d) 9