Let PQ be a focal chord of the parabola y2=4ax The tangents to the parabola at P and Q meet at a point lying on the line y=2x+a,a>0. Length of chord PQ is
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Two circles are given such that one is completely lying inside the other without touching. Prove that the locus of the center of variable circle which touches the smaller circle from outside and the bigger circle from inside is an ellipse.
Find the equation of the circle with centre (0,2) and radius 2
Find the equation of the circle with centre (−a,−b) and radius a2−b2
Find the equation of the circle with centre (1,1) and radius 2
Find the point on the hyperbola x2−9y2=9
where the line 5x+12y=9
Find the equation of the chord of the hyperbola 25x2−16y2=400
which is bisected at the point (5, 3).
Find the foci of the ellipse 25(x+1)2+9(y+2)2=225.
If (5, 12) and (24, 7) are the foci of an ellipse passing through the origin, then find the eccentricity of the ellipse.