The common tangents to the circle x2+y2=2 and the parabola y2=8x touch the circle at P,Q andthe parabola at R,S. Then area of quadrilateral PQRS is
If x1,x2,x3 as well as y1,y2,y3 are in GP with the same common ratio, then the points (x1,y1),(x2,y2), and (x3,y3)˙ lie on a straight line lie on an ellipse lie on a circle (d) are the vertices of a triangle.
Through the point P(α,β) , where αβ>0, the straight line ax+by=1 is drawn so as to form a triangle of area S with the axes. If ab>0, then the least value of S is αβ (b) 2αβ (c) 3αβ (d) none
Plot the points given in the following table on the plane, choosing suitable units of distance on the axes.
Given that A1,A2,A3,An are n points in a plane whose coordinates are x1,y1),(x2,y2),(xn,yn), respectively. A1A2 is bisected at the point P1,P1A3 is divided in the ratio A:2 at P2,P2A4 is divided in the ratio 1:3 at P3,P3A5 is divided in the ratio 1:4 at P4 , and so on until all n points are exhausted. Find the final point so obtained.
The three points (−2,2)(9,−2),and(−4,−3) are the vertices of (a) an isosceles triangle (b) an equilateral triangle (c) a right-angled triangle (d) none of these