The number of common tangents to the circles x2+y2-4x-6y-12=0 and x2+y2+6x+18y+26=0, is :
Orthocenter and circumcenter of a DeltaABC are (a,b)and(c,d) , respectively. If the coordinates of the vertex A are (x1,y1), then find the coordinates of the middle point of BC˙
What does the equation 2x2+4xy−5y2+20x−22y−14=0 become when referred to the rectangular axes through the point (−2,−3) , the new axes being inclined at an angle at 450 with the old axes?
Find the area of the triangle formed by the lines joining the vertex of the parabola x2=12yto the ends of its latus rectum.
If ABC having vertices A(acosθ1,asinθ1),B(acosθ2asinθ2),andC(acosθ3,asinθ3) is equilateral, then prove that cosθ1+cosθ2+cosθ3=sinθ1+sinθ2+sinθ3=0.
In Fig. 10.39, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠BEC = 130o and ∠ECD = 20⊙ Find ∠BAC˙