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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Find the equation of the parabola with vertex at origin, symmetric with respect to y-axis and passing through (2,−3)
A variable line through point P(2,1)
meets the axes at AandB
. Find the locus of the circumcenter of triangle OAB
is the origin).
Given the equation 4x2+23xy+2y2=1
. Through what angle should the axes be rotated so that the term xy
is removed from the transformed equation.
A point moves such that the area of the triangle formed by it with the points (1, 5) and (3,−7)is21squ˙nits˙ Then, find the locus of the point.
Two points O(0,0)
with another point P
form an equilateral triangle. Find the coordinates of P˙
having vertices A(acosθ1,asinθ1),B(acosθ2asinθ2),andC(acosθ3,asinθ3)
is equilateral, then prove that cosθ1+cosθ2+cosθ3=sinθ1+sinθ2+sinθ3=0.
Find the equation of the parabola that satisfies the given conditions:Vertex (0,0) passing through (2,3) arid axis is along x–axis.
Find the equation of the parabola that satisfies the given conditions:Focus (0,3); directrix y=3