For how many values, of p, the circle x2+y2+2x+4y−p=0and the coordinate axes have exactly three common points?
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If (xi,yi),i=1,2,3, are the vertices of an equilateral triangle such that (x1+2)2+(y1−3)2=(x2+2)2+(y2−3)2=(x3+2)2+(y3−3)2, then find the value of y1+y2+y3x1+x2+x3 .
Express the polar equation r=2cosθ in rectangular coordinates.
Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
In ABC Prove that AB2+AC2=2(AO2+BO2) , where O is the middle point of BC
If a vertex, the circumcenter, and the centroid of a triangle are (0, 0), (3,4), and (6, 8), respectively, then the triangle must be (a) a right-angled triangle (b) an equilateral triangle (c) an isosceles triangle (d) a right-angled isosceles triangle
into a polar equation.
If the middle points of the sides of a triangle are (−2,3),(4,−3),and(4,5)
, then find the centroid of the triangle.
Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.