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

Find the curve for which the length of normal is equal to the radius vector.

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

The locus of a point which moves such that the sum of the square of its distance from three vertices of a triangle is constant is a/an (a)circle (b) straight line (c) ellipse (d) none of these

The locus of the point of intersection of the tangent at the endpoints of the focal chord of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 ( b < a) (a) is a an circle (b) ellipse (c) hyperbola (d) pair of straight lines

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

A circle touches the x-axis and also thouches the circle with center (0, 3) and radius 2. The locus of the center of the circle is (a)a circle (b) an ellipse (c)a parabola (d) a hyperbola

The curve with the property that the projection of the ordinate on the normal is constant and has a length equal to a is

Consider two straight lines, each of which is tangent to both the circle x^2+y^2=1/2 and the parabola y^2=4x . Let these lines intersect at the point Q . Consider the ellipse whose center is at the origin O(0,\ 0) and whose semi-major axis is O Q . If the length of the minor axis of this ellipse is sqrt(2) , then which of the following statement(s) is (are) TRUE? For the ellipse, the eccentricity is 1/(sqrt(2)) and the length of the latus rectum is 1 (b) For the ellipse, the eccentricity is 1/2 and the length of the latus rectum is 1/2 (c) The area of the region bounded by the ellipse between the lines x=1/(sqrt(2)) and x=1 is 1/(4sqrt(2))(pi-2) (d) The area of the region bounded by the ellipse between the lines x=1/(sqrt(2)) and x=1 is 1/(16)(pi-2)

The perimeter of certain sector of a circle is equal to the length of the a semi-circle having the same radius. Express the angle of the sector in degress, minutes and seconds.